Homology

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Singular Homology Theory

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Author : W.S. Massey
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Singular Homology Theory written by W.S. Massey 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 textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind various algebraic concepts is emphasized. The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory.

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.

Homology

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Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Homology written by Saunders MacLane 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.

In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Computational Homology

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Author : Tomasz Kaczynski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18

Computational Homology written by Tomasz Kaczynski 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 2006-04-18 with Mathematics categories.

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

Strong Shape And Homology

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Author : Sibe Mardesic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Strong Shape And Homology written by Sibe Mardesic 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 2013-03-14 with Mathematics categories.

Shape theory, an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces, was introduced by Borsuk 30 years ago and Mardesic contributed greatly to it. One expert says: "If we need a book in the field, this is it! It is thorough, careful and complete."

Cyclic Homology

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Author : Jean-Louis Loday
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Cyclic Homology written by Jean-Louis Loday 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 2013-03-09 with Mathematics categories.

From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.

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

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Author : Brian K. Hall
language : en
Publisher: Academic Press
Release Date : 2012-12-02

Homology written by Brian K. Hall and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.

Homology, the similarity between organisms that is due to common ancestry, is the central concept of all comparative biology. However, the application of this concept varies depending on the data being examined. This volume represents a state-of-the-art treatment of the different applications of this unifying concept. Chapters deal with homology on all levels, from molecules to behavior, and are authored by leading contributors to systematics, natural history, and evolutionary, developmental, and comparative biology. Commemoration of the 150th anniverary of Sir Richard Owen's seminal paper distinguishing homology from analogy Contributors who are renowned leaders in compative biology Coverage that is both comprehensive and interdisciplinary

Homology Theory On Algebraic Varieties

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Author : Andrew H. Wallace
language : en
Publisher: Courier Corporation
Release Date : 2014-10-27

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 2014-10-27 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.

Algebraic Topology Homology And Cohomology

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Author : Andrew H. Wallace
language : en
Publisher:
Release Date : 1970

Algebraic Topology Homology And Cohomology written by Andrew H. Wallace and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

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.