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Elements of Homology Theory

2007 Mathematics
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Release : 2007
Genre : Mathematics
Kind : eBook
Book Rating : 121/5 ( reviews)

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Book Synopsis Elements of Homology Theory by : Viktor Vasilʹevich Prasolov

Download or read book Elements of Homology Theory written by Viktor Vasilʹevich Prasolov. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: 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

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 182/5 ( reviews)

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Book Synopsis Elements of Homotopy Theory by : George W. Whitehead

Download or read book Elements of Homotopy Theory written by George W. Whitehead. This book was released on 2012-12-06. 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.

Elements Of Algebraic Topology

2018-03-05 Mathematics
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Release : 2018-03-05
Genre : Mathematics
Kind : eBook
Book Rating : 460/5 ( reviews)

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Book Synopsis Elements Of Algebraic Topology by : James R. Munkres

Download or read book Elements Of Algebraic Topology written by James R. Munkres. This book was released on 2018-03-05. 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.

Completion, Čech and Local Homology and Cohomology

2018-09-15 Mathematics
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Release : 2018-09-15
Genre : Mathematics
Kind : eBook
Book Rating : 174/5 ( reviews)

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Book Synopsis Completion, Čech and Local Homology and Cohomology by : Peter Schenzel

Download or read book Completion, Čech and Local Homology and Cohomology written by Peter Schenzel. This book was released on 2018-09-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in the Homology Theory of Fibre Bundles

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 758/5 ( reviews)

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Book Synopsis Topics in the Homology Theory of Fibre Bundles by : Armand Borel

Download or read book Topics in the Homology Theory of Fibre Bundles written by Armand Borel. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt:

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