Basic Algebraic Topology

Author : Anant R. Shastri
Publisher : CRC Press
ISBN 13 : 1466562447
Total Pages : 552 pages
Book Rating : 4.48/5 ( download)

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Download or read book Basic Algebraic Topology written by Anant R. Shastri and published by CRC Press. This book was released on 2016-02-03 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si

Author : Mahima Ranjan Adhikari
Publisher : Springer
ISBN 13 : 813222843X
Total Pages : 615 pages
Book Rating : 4.31/5 ( download)

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Download or read book Basic Algebraic Topology and its Applications written by Mahima Ranjan Adhikari and published by Springer. This book was released on 2016-09-16 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Author : William S. Massey
Publisher : Springer
ISBN 13 : 1493990632
Total Pages : 448 pages
Book Rating : 4.34/5 ( download)

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Download or read book A Basic Course in Algebraic Topology written by William S. Massey and published by Springer. This book was released on 2019-06-28 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

Author : Fred H. Croom
Publisher :
ISBN 13 : 9783540902881
Total Pages : 177 pages
Book Rating : 4.80/5 ( download)

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Download or read book Basic Concepts of Algebraic Topology written by Fred H. Croom and published by . This book was released on 1978 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text traces the development of algebraic topology form its inception in 1895 through the development of singular homology theory. Primary topics include geometric complexes, simplicial homology groups, simplicial mappings, the fundamental group, covering spaces, and introductory singular homology theory, as well as the higher homotopy groups and the homology sequence--two areas seldom covered in introductory text. The author develops many important applications, including the fixed point theorems of Brouwer and Lefschetz, vector fields on spheres, and the covering homotopy property.

Author : Allen Hatcher
Publisher : Cambridge University Press
ISBN 13 : 9780521795401
Total Pages : 572 pages
Book Rating : 4.00/5 ( download)

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Download or read book Algebraic Topology written by Allen Hatcher and published by Cambridge University Press. This book was released on 2002 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Author : Andrew H. Wallace
Publisher : Courier Corporation
ISBN 13 : 0486152952
Total Pages : 212 pages
Book Rating : 4.50/5 ( download)

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Download or read book An Introduction to Algebraic Topology written by Andrew H. Wallace and published by Courier Corporation. This book was released on 2011-11-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.39/5 ( download)

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Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : C. R. F. Maunder
Publisher : Courier Corporation
ISBN 13 : 9780486691312
Total Pages : 414 pages
Book Rating : 4.14/5 ( download)

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Download or read book Algebraic Topology written by C. R. F. Maunder and published by Courier Corporation. This book was released on 1996-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.

Author : Mahima Ranjan Adhikari
Publisher : Springer Nature
ISBN 13 : 9811665508
Total Pages : 488 pages
Book Rating : 4.09/5 ( download)

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Download or read book Basic Topology 3 written by Mahima Ranjan Adhikari and published by Springer Nature. This book was released on 2023-03-15 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.

Author : M. A. Armstrong
Publisher :
ISBN 13 : 9781475717945
Total Pages : 272 pages
Book Rating : 4.46/5 ( download)

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Download or read book Basic Topology written by M. A. Armstrong and published by . This book was released on 2014-01-15 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: