Algebraic Topology An Intuitive Approach
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Algebraic Topology An Intuitive Approach
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Author : Hajime Satō
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Algebraic Topology An Intuitive Approach written by Hajime Satō 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 1999 with Mathematics categories.
Develops an introduction to algebraic topology mainly through simple examples built on cell complexes. Topics covers include homeomorphisms, topological spaces and cell complexes, homotopy, homology, cohomology, the universal coefficient theorem, fiber bundles and vector bundles, and spectral sequences. Includes chapter summaries, exercises, and answers. Includes an appendix of definitions in sets, topology, and groups. Originally published in Japanese by Iwanami Shoten, Publishers, Tokyo, 1996. Annotation copyrighted by Book News, Inc., Portland, OR
Algebraic Topology
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Author : Hajime Satō
language : en
Publisher:
Release Date : 1999
Algebraic Topology written by Hajime Satō and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Algebraic topology categories.
A Concise Course In Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 1999-09
A Concise Course In Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09 with Mathematics categories.
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Homology Theory
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Author : James W. Vick
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-01-07
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 1994-01-07 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.
An Introduction To Algebraic Topology
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Author : Andrew H. Wallace
language : en
Publisher: Courier Corporation
Release Date : 2007-02-27
An Introduction To Algebraic Topology 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 2007-02-27 with Mathematics categories.
Originally published: Homology theory on algebraic varieties. New York: Pergamon Press, 1957.
Homotopy Theory An Introduction To Algebraic Topology
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Author :
language : en
Publisher: Academic Press
Release Date : 1975-11-12
Homotopy Theory An Introduction To Algebraic Topology written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-11-12 with Mathematics categories.
Homotopy Theory: An Introduction to Algebraic Topology
Algebraic Topology
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Author : Tammo tom Dieck
language : en
Publisher: European Mathematical Society
Release Date : 2008
Algebraic Topology written by Tammo tom Dieck and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.
Differential Algebraic Topology
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Author : Matthias Kreck
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Differential Algebraic Topology written by Matthias Kreck 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 2010 with Mathematics categories.
This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres. This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.
Lecture Notes In Algebraic Topology
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Author : James Frederic Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lecture Notes In Algebraic Topology written by James Frederic Davis 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 2001 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic andgeometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, someknowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstructiontheory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to presentproofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, andhomological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Combinatorial Algebraic Topology
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Author : Dimitry Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-29
Combinatorial Algebraic Topology written by Dimitry Kozlov 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 2007-12-29 with Mathematics categories.
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.