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Algebraic Topology

A Primer

  • Textbook
  • © 2018

Overview

Authors:
  1. Satya Deo

    1. Harish-Chandra Research Institute, Allahabad, India

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  • Presents revised and enlarged concepts of the topics in algebraic topology
  • Contains several exercises from elementary to proficient level
  • Is written by author having over 40 years of teaching experience
  • Is useful to undergraduate and graduate students of mathematics

Part of the book series: Texts and Readings in Mathematics (TRIM, volume 27)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Basic Topology: a review

    • Satya Deo
    Pages 1-34

  3. The Fundamental Group

    • Satya Deo
    Pages 35-81

  4. Simplicial Complexes

    • Satya Deo
    Pages 83-122

  5. Simplicial Homology

    • Satya Deo
    Pages 123-198

  6. Covering Projections

    • Satya Deo
    Pages 199-225

  7. Singular Homology

    • Satya Deo
    Pages 227-294

  8. Appendix

    • Satya Deo
    Pages 295-338

  9. Back Matter

    Pages i-xiii
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Keywords

About this book

This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces.

The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes challenging, for the reader to provoke their curiosity for problem-solving.

Authors and Affiliations

  • Harish-Chandra Research Institute, Allahabad, India

    Satya Deo

About the author

SATYA DEO is senior scientist at the National Academy of Sciences, India, and honorary professor at Harish-Chandra Research Institute, Allahabad, India. He was awarded the Distinguished Service Award by the Mathematical Association of India for outstanding contributions to the cause of teaching and research in 2006 and the Indian Science Congress Gold Medal by the Prime Minister of India, in 2010. He has guided 17 PhD students and published over 70 papers in reputed international journals and proceedings. His area of specialization includes algebraic and differential topology, topological and differentiable group actions, homology-cohomology theories, cohomological dimesion theory, burnside rings, hopfian and cohopfian rings, spline modules and topological combinatorics.

Bibliographic Information

  • Book Title: Algebraic Topology

  • Book Subtitle: A Primer

  • Authors: Satya Deo

  • Series Title: Texts and Readings in Mathematics

  • DOI: https://doi.org/10.1007/978-981-10-8734-9

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2018

  • eBook ISBN: 978-981-10-8734-9Published: 13 March 2018

  • Series ISSN: 2366-8717

  • Series E-ISSN: 2366-8725

  • Edition Number: 2

  • Number of Pages: XII, 344

  • Number of Illustrations: 104 b/w illustrations

  • Topics: Algebraic Topology

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