Download or read book Topological Library Characteristic classes and smooth structures on manifolds written by Serge? Petrovich Novikov and published by World Scientific. This book was released on 2009-10-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s?1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated ?singular homologies of fiber spaces.?
Download or read book Topological Library written by Sergeĭ Petrovich Novikov and published by World Scientific. This book was released on 2010 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. On manifolds homeomorphic to the 7-sphere / J. Milnor -- 2. Groups of homotopy spheres. I / M. Kervaire and J. Milnor -- 3. Homotopically equivalent smooth manifolds / S.P. Novikov -- 4. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds / S.P. Novikov -- 5. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) / S.P. Novikov -- 6. Stable homeomorphisms and the annulus conjecture / R. Kirby
Download or read book Topological Library Part 2 Characteristic Classes And Smooth Structures On Manifolds written by Serguei Petrovich Novikov and published by World Scientific. This book was released on 2009-10-07 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”
Download or read book Topological Library written by Сергей Петрович Новиков and published by World Scientific Publishing Company. This book was released on 2007 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. On manifolds homeomorphic to the 7-sphere / J. Milnor -- 2. Groups of homotopy spheres. I / M. Kervaire and J. Milnor -- 3. Homotopically equivalent smooth manifolds / S.P. Novikov -- 4. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds / S.P. Novikov -- 5. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) / S.P. Novikov -- 6. Stable homeomorphisms and the annulus conjecture / R. Kirby
Download or read book Characteristic Classes and Smooth Structures on Manifolds written by and published by . This book was released on 2010 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characteristic Classes written by John Willard Milnor and published by Princeton University Press. This book was released on 1974 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Download or read book The Topology of 4 Manifolds written by Robion C. Kirby and published by Springer. This book was released on 2006-11-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.
Download or read book Piecewise Linear Structures On Topological Manifolds written by Yuli Rudyak and published by World Scientific. This book was released on 2015-12-28 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture.The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking.
Download or read book Introduction to Smooth Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Download or read book Smooth S1 Manifolds written by Wolf Iberkleid and published by Springer. This book was released on 1976 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological Library written by Serge? Petrovich Novikov and published by World Scientific. This book was released on 2012 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in 1950-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated "singular homologies of fiber spaces."
Download or read book Topological Library Part 3 Spectral Sequences In Topology written by Serguei Petrovich Novikov and published by World Scientific. This book was released on 2012-07-25 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.”
Download or read book Smooth Four Manifolds and Complex Surfaces written by Robert Friedman and published by Springer Science & Business Media. This book was released on 1994-03-10 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
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 Scientific Legacy Of Professor Zbigniew Oziewicz Selected Papers From The International Conference Applied Category Theory Graph operad logic written by Hilda Maria Colin Garcia and published by World Scientific. This book was released on 2023-09-27 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy.Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science.The book is laid out in twelve main topics where we can find relevant works from distinguished experts.
Download or read book New Horizons For Second order Cybernetics written by Alexander Riegler and published by World Scientific. This book was released on 2017-09-15 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: In almost 60 articles this book reviews the current state of second-order cybernetics and investigates which new research methods second-order cybernetics can offer to tackle wicked problems in science and in society. The contributions explore its application to both scientific fields (such as mathematics, psychology and consciousness research) and non-scientific ones (such as design theory and theater science). The book uses a pluralistic, multifaceted approach to discuss these applications: Each main article is accompanied by several commentaries and author responses, which together allow the reader to discover further perspectives than in the original article alone. This procedure shows that second-order cybernetics is already on its way to becoming an idea shared by many researchers in a variety of disciplines.
Download or read book Quipu Decorated Permutation Representations Of Finite Groups written by Yongju Bae and published by World Scientific. This book was released on 2024-06-27 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
