Download or read book Simplicial Methods for Operads and Algebraic Geometry written by Ieke Moerdijk and published by Springer Science & Business Media. This book was released on 2010-12-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword

Download or read book Simplicial and Operad Methods in Algebraic Topology written by Vladimir Alekseevich Smirnov and published by American Mathematical Soc.. This book was released on 2001 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, for solving problems of algebraic topology and, in particular, difficult problems of homotopy theory, algebraic structures more complicated than just a topological monoid, an algebra, a coalgebra, etc., have been used more and more often. A convenient language for describing various structures arising naturally on topological spaces and on their cohomology and homotopy groups is the language of operads and algebras over an operad. This language was proposed by J. P. May in the 1970s to describe the structures on various loop spaces. This book presents a detailed study of the concept of an operad in the categories of topological spaces and of chain complexes. The notions of an algebra and a coalgebra over an operad are introduced, and their properties are investigated. The algebraic structure of the singular chain complex of a topological space is explained, and it is shown how the problem of homotopy classification of topological spaces can be solved using this structure. For algebras and coalgebras over operads, standard constructions are defined, particularly the bar and cobar constructions. Operad methods are applied to computing the homology of iterated loop spaces, investigating the algebraic structure of generalized cohomology theories, describing cohomology of groups and algebras, computing differential in the Adams spectral sequence for the homotopy groups of the spheres, and some other problems.

Download or read book Homotopy of Operads and Grothendieck Teichmuller Groups written by Benoit Fresse and published by American Mathematical Soc.. This book was released on 2017-05-22 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.

Download or read book Simplicial Objects in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1992 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simplicial sets are discrete analogs of topological spaces. They have played a central role in algebraic topology ever since their introduction in the late 1940s, and they also play an important role in other areas such as geometric topology and algebraic geometry. On a formal level, the homotopy theory of simplicial sets is equivalent to the homotopy theory of topological spaces. In view of this equivalence, one can apply discrete, algebraic techniques to perform basic topological constructions. These techniques are particularly appropriate in the theory of localization and completion of topological spaces, which was developed in the early 1970s. Since it was first published in 1967, Simplicial Objects in Algebraic Topology has been the standard reference for the theory of simplicial sets and their relationship to the homotopy theory of topological spaces. J. Peter May gives a lucid account of the basic homotopy theory of simplicial sets, together with the equivalence of homotopy theories alluded to above. The central theme is the simplicial approach to the theory of fibrations and bundles, and especially the algebraization of fibration and bundle theory in terms of "twisted Cartesian products." The Serre spectral sequence is described in terms of this algebraization. Other topics treated in detail include Eilenberg-MacLane complexes, Postnikov systems, simplicial groups, classifying complexes, simplicial Abelian groups, and acyclic models. "Simplicial Objects in Algebraic Topology presents much of the elementary material of algebraic topology from the semi-simplicial viewpoint. It should prove very valuable to anyone wishing to learn semi-simplicial topology. [May] has included detailed proofs, and he has succeeded very well in the task of organizing a large body of previously scattered material."—Mathematical Review

Download or read book Lectures on Algebraic Topology written by Sergeĭ Vladimirovich Matveev and published by European Mathematical Society. This book was released on 2006 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

Download or read book Alpine Perspectives on Algebraic Topology written by Christian Ausoni and published by American Mathematical Soc.. This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.

Download or read book Algebraic Topology written by Max K. Agoston and published by . This book was released on 1976 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Topology of Finite Topological Spaces and Applications written by Jonathan A. Barmak and published by Springer. This book was released on 2011-08-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.

Download or read book Algebraic Topology written by Edwin H. Spanier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Download or read book Algebraic and Geometrical Methods in Topology written by L.F. McAuley and published by Springer. This book was released on 2006-11-15 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Homotopy Methods in Algebraic Topology written by Nicholas Kuhn and published by American Mathematical Soc.. This book was released on 2001-04-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.

Download or read book Combinatorial Algebraic Topology written by Dimitry Kozlov and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Download or read book Simplicial Objects in Algebraic Topology written by Peter J. May and published by . This book was released on 1992 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elements Of Algebraic Topology written by James R. Munkres and published by CRC Press. This book was released on 2018-03-05 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.

Download or read book Simplicial Structures in Topology written by Davide L. Ferrario and published by Springer Science & Business Media. This book was released on 2010-09-30 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henry Poincaré (singular homology is discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful.

Download or read book Algebraic Topology written by Satya Deo and published by Springer. This book was released on 2003-12-01 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Topology Homology and Cohomology written by Andrew H. Wallace and published by . This book was released on 1970 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is suitable for advanced undergraduate and graduate students and may be used either after or concurrently with courses in general topology and algebra. It surveys several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomology groups. Proceeding from the view of topology as a form of geometry, Wallace emphasizes geometrical motivations and interpretations. Once beyond the singular homology groups, however, the author advances an understanding of the subject's algebraic patterns, leaving geometry aside in order to study these patterns as pure algebra. Numerous exercises appear throughout the text. In addition to developing students' thinking in terms of algebraic topology, the exercises also unify the text, since many of them feature results that appear in later expositions. Extensive appendixes offer helpful reviews of background material.