Elements Of Homology Theory
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Elements Of Homology Theory
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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Elements Of Homology Theory written by Viktor Vasilʹevich Prasolov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.
Elements Of Homotopy Theory
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Author : George W. Whitehead
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elements Of Homotopy Theory written by George W. Whitehead and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Elements Of Algebraic Topology
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Author : James R. Munkres
language : en
Publisher: CRC Press
Release Date : 2018-03-05
Elements Of Algebraic Topology written by James R. Munkres and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Mathematics categories.
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.
Homology Theory
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Author : P. J. Hilton
language : en
Publisher: CUP Archive
Release Date : 1967
Homology Theory written by P. J. Hilton and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.
Homology Theory
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Author : James W. Vick
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homology Theory written by James W. Vick and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
Topics In The Homology Theory Of Fibre Bundles
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Author : Armand Borel
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In The Homology Theory Of Fibre Bundles written by Armand Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
A Geometric Approach To Homology Theory
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Author : S. Buoncristiano
language : en
Publisher: Cambridge University Press
Release Date : 1976-04
A Geometric Approach To Homology Theory written by S. Buoncristiano and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-04 with Mathematics categories.
The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.
Homology Theory On Algebraic Varieties
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Author : Andrew H. Wallace
language : en
Publisher: Courier Corporation
Release Date : 2015-01-14
Homology Theory On Algebraic Varieties written by Andrew H. Wallace and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-14 with Mathematics categories.
Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and relative cycles. 1958 edition.
Homology Of Linear Groups
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Author : Kevin P. Knudson
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Homology Of Linear Groups written by Kevin P. Knudson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation. It presents the stability theorems and low-dimensional results of A. Suslin, W. van der Kallen and others are presented. Coverage also examines the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete.
Completion Ech And Local Homology And Cohomology
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Author : Peter Schenzel
language : en
Publisher: Springer
Release Date : 2018-09-15
Completion Ech And Local Homology And Cohomology written by Peter Schenzel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-15 with Mathematics categories.
The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Čech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.