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Algebraic Topology

A Primer

  • Satya Deo

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Satya Deo
    Pages 1-34
  3. Satya Deo
    Pages 35-81
  4. Satya Deo
    Pages 83-122
  5. Satya Deo
    Pages 123-198
  6. Satya Deo
    Pages 199-225
  7. Satya Deo
    Pages 227-294
  8. Satya Deo
    Pages 295-338
  9. Back Matter
    Pages i-xiii

About this book

Introduction

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.

Keywords

general simplicial complexes simplicial homology theory fundamental groups covering spaces singular homology theory

Authors and affiliations

  • Satya Deo
    • 1
  1. 1.Harish-Chandra Research InstituteAllahabadIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-8734-9
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018 and Hindustan Book Agency 2018 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-981-10-8734-9
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • Buy this book on publisher's site