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.

Table of Contents

1 Basic Topology: a review

2 The Fundamental Group

3 Simplicial Complexes

4 Simplicial Homology

5 Covering Projections

6 Singular Homology

7 Appendix

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.