Download or read book Three Dimensional Geometry and Topology Volume 1 written by William P. Thurston and published by Princeton University Press. This book was released on 2014-10-31 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Download or read book Topology and Geometry in Dimension Three written by Weiping Li and published by American Mathematical Soc.. This book was released on 2011 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Download or read book Topology and Geometry in Dimension Three written by Weiping Li and published by American Mathematical Soc.. This book was released on 2011 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Download or read book The Geometry and Topology of Three Manifolds written by William P. Thurston and published by American Mathematical Society. This book was released on 2022-07-19 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.

Download or read book Three dimensional Geometry and Topology written by William P. Thurston and published by Princeton Mathematical Series. This book was released on 1997 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.

Download or read book Elements of the geometry and topology of minimal surfaces in three dimensional space written by A. T. Fomenko and published by American Mathematical Soc.. This book was released on 2005 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.

Download or read book Geometric Topology in Dimensions 2 and 3 written by E.E. Moise and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.

Download or read book Three dimensional geometry topology written by William P. Thurston and published by . This book was released on 1991 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry and Topology in Dynamics written by Marcy Barge and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua. New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.

Download or read book Symplectic Geometry and Topology written by Yakov Eliashberg and published by American Mathematical Soc.. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Download or read book Low Dimensional Topology written by Tomasz Mrowka and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.

Download or read book Lectures on Quantum Topology in Dimension Three written by Thang T. Q. Lê and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains three lecture series from the SMF school Geometric and Quantum Topology in Dimension 3, which was held at CIRM in June 2014. These lectures are introduced by a partial survey of the history of these invariants and present recent progress on the study of 3-manifold and link invariants.

Download or read book Visual Geometry and Topology written by Anatolij T. Fomenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and topology are strongly motivated by the visualization of ideal objects that have certain special characteristics. A clear formulation of a specific property or a logically consistent proof of a theorem often comes only after the mathematician has correctly "seen" what is going on. These pictures which are meant to serve as signposts leading to mathematical understanding, frequently also contain a beauty of their own. The principal aim of this book is to narrate, in an accessible and fairly visual language, about some classical and modern achievements of geometry and topology in both intrinsic mathematical problems and applications to mathematical physics. The book starts from classical notions of topology and ends with remarkable new results in Hamiltonian geometry. Fomenko lays special emphasis upon visual explanations of the problems and results and downplays the abstract logical aspects of calculations. As an example, readers can very quickly penetrate into the new theory of topological descriptions of integrable Hamiltonian differential equations. The book includes numerous graphical sheets drawn by the author, which are presented in special sections of "Visual material". These pictures illustrate the mathematical ideas and results contained in the book. Using these pictures, the reader can understand many modern mathematical ideas and methods. Although "Visual Geometry and Topology" is about mathematics, Fomenko has written and illustrated this book so that students and researchers from all the natural sciences and also artists and art students will find something of interest within its pages.

Download or read book A Ludic Journey into Geometric Topology written by Ton Marar and published by Springer Nature. This book was released on 2022-09-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book draws on elements from everyday life, architecture, and the arts to provide the reader with elementary notions of geometric topology. Pac Man, subway maps, and architectural blueprints are the starting point for exploring how knowledge about geometry and, more specifically, topology has been consolidated over time, offering a learning journey that is both dense and enjoyable. The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories that explain the Cosmos. Geometry from Felix Klein's point of view is then presented, paving the way to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, as well as hypersurface models. Adopting a style that is both rigorous and accessible, this book will appeal to a broad audience, from curious students and researchers in various areas of knowledge to everyone who feels instigated by the power of mathematics in representing our world - and beyond.

Download or read book Different Faces of Geometry written by Simon Donaldson and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvath (USA) and Z. Szabo (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in low-dimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvath and Szabo). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun.Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Kahler and algebraic manifolds), a point which is also made by Bauer in the context of 4-manifolds and the 11/8 conjecture. LeBrun's article gives another perspective on 4-manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even well-known 4-manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the geometry is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra.The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebro-topological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems. - From the Preface by the Editors

Download or read book New Ideas In Low Dimensional Topology written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2015-01-27 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.

Download or read book Geometry In Our Three dimensional World written by Alfred S Posamentier and published by World Scientific. This book was released on 2021-11-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.