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Homotopy Type And Homology
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Book Synopsis Homotopy Type and Homology by : Hans J. Baues
Download or read book Homotopy Type and Homology written by Hans J. Baues and published by Oxford University Press. This book was released on 1996 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph represents an attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classifications, and includes applications to the classification of manifolds.
Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :
Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homotopy Theory written by I. M. James and published by Elsevier. This book was released on 2014-05-09 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.
Book Synopsis Stable Homotopy and Generalised Homology by : John Frank Adams
Download or read book Stable Homotopy and Generalised Homology written by John Frank Adams and published by University of Chicago Press. This book was released on 1974 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Book Synopsis Homotopy Theoretic Methods in Group Cohomology by : William G. Dwyer
Download or read book Homotopy Theoretic Methods in Group Cohomology written by William G. Dwyer and published by Birkhäuser. This book was released on 2012-12-06 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
Book Synopsis Handbook of Algebraic Topology by : I.M. James
Download or read book Handbook of Algebraic Topology written by I.M. James and published by Elsevier. This book was released on 1995-07-18 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.
Book Synopsis Combinatorial Homotopy and 4-Dimensional Complexes by : Hans-Joachim Baues
Download or read book Combinatorial Homotopy and 4-Dimensional Complexes written by Hans-Joachim Baues and published by Walter de Gruyter. This book was released on 2011-05-12 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Book Synopsis Homotopy Theory: An Introduction to Algebraic Topology by :
Download or read book Homotopy Theory: An Introduction to Algebraic Topology written by and published by Academic Press. This book was released on 1975-11-12 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Theory: An Introduction to Algebraic Topology
Book Synopsis Elements of Homotopy Theory by : George W. Whitehead
Download or read book Elements of Homotopy Theory written by George W. Whitehead and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.
Book Synopsis Rational Homotopy Theory by : Yves Felix
Download or read book Rational Homotopy Theory written by Yves Felix and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Book Synopsis Equivariant Homotopy and Cohomology Theory by : J. Peter May
Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Book Synopsis Cohomology Operations and Applications in Homotopy Theory by : Robert E. Mosher
Download or read book Cohomology Operations and Applications in Homotopy Theory written by Robert E. Mosher and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Book Synopsis Introduction to Homotopy Theory by : Paul Selick
Download or read book Introduction to Homotopy Theory written by Paul Selick and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Book Synopsis Rational Homotopy Type by : Wen-tsün Wu
Download or read book Rational Homotopy Type written by Wen-tsün Wu and published by Springer. This book was released on 2006-11-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph provides a self-contained treatment of the theory of I*-measure, or Sullivan's rational homotopy theory, from a constructive point of view. It centers on the notion of calculability which is due to the author himself, as are the measure-theoretical and constructive points of view in rational homotopy. The I*-measure is shown to differ from other homology and homotopy measures in that it is calculable with respect to most of the important geometric constructions encountered in algebraic topology. This approach provides a new method of treatment and leads to various new results. In particular, an axiomatic system of I*-measure is formulated, quite different in spirit from the usual Eilenberg-Steenrod axiomatic system for homology, and giving at the same time an algorithmic method of computation of the I*-measure in concrete cases. The book will be of interest to researchers in rational homotopy theory and will provide them with new ideas and lines of research to develop further.
Book Synopsis Counterexamples in Topology by : Lynn Arthur Steen
Download or read book Counterexamples in Topology written by Lynn Arthur Steen and published by Courier Corporation. This book was released on 2013-04-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Book Synopsis Algebraic Topology by : Edwin H. Spanier
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.
Book Synopsis Homotopy Theory and Models by : Marc Aubry
Download or read book Homotopy Theory and Models written by Marc Aubry and published by Birkhäuser. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In keeping with the general aim of the "D.M.V.-Seminar" series, this book is princi pally a report on a group of lectures held at Blaubeuren by Professors H. J. Baues, S. Halperin and J.-M. Lemaire, from October 30 to November 7, 1988. These lec tures were devoted to providing an introduction to the theory of models in algebraic homotopy. The three lecturers acted in concert to produce a coherent exposition of the theory. Commencing from a common starting point, each of them then proceeded naturally to his own subject of research. The reader who is already familiar with their scientific work will certainly give the lecturers their due. Having been asked by the speakers to take on the responsibility of writing down the notes, it seemed to me that the material elucidated in the short span of fifteen hours was too dense to appear, unedited, in book form. Some amplification was necessary. Of course I submitted to them the final version of this book, which received their approval. I thank them for this token of confidence. I am also grateful to all three for their help and advice in writing this book. I am particularly indebted to J.-M. Lemaire who was indeed very often consulted. For basic notions (in particular those concerning homotopy groups, CW complexes, (co)homology and homological algebra) the reader is advised to refer to the fundamental books written by E. H. Spanier [47], R. M. Switzer [49] and G. Whitehead [52].
