Overview
Discusses the basic concepts of algebraic topology with numerous related illustrations and applications
Approaches the topic nearly “from scratch” and accompanies students through its natural development
Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic
Integrates various concepts of algebraic topology, examples, exercises, applications, and historical notes
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 pursue further study
Includes supplementary material: sn.pub/extras
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Table of contents (18 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“Adhikari’s work is an excellent resource for any individual seeking to learn more about algebraic topology. By no means will this text feel like an introduction to algebraic topology, but it does offer much for both beginners and experts. … the text will be a valuable reference on the bookshelf of any reader with an interest in algebraic topology. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (A. Misseldine, Choice, Vol. 54 (9), May, 2017)
“I am pretty enthusiastic about this book. … it shows very good taste on the author’s part as far as what he’s chosen to do and how he’s chosen to do it. … Wow! What a nice book. I’m glad I have a copy.” (Michael Berg, MAA Reviews, maa.org, February, 2017)
“This is a comprehensive textbook on algebraic topology. … accessible to students of all levels of mathematics, so suitable for anyone wanting and needing to learn about algebraic topology. It can also offer a valuable resource for advanced students with a specialized knowledge in other areas who want to pursue their interest in this area. … further readings are provided at the end of each of them, which also enables students to study the subject discussed therein in more depth.” (Haruo Minami, zbMATH 1354.55001, 2017)
Authors and Affiliations
About the author
He has visited several institutions in India, USA, UK, Japan, France, Greece, Sweden, Switzerland, Italy and many other countries on invitation. While visiting E.T.H., Zurich, Switzerland, in 2003, he made an academic interaction with Professor B Eckmann and P J Hilton. He is currently the president of the Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC). He is also the principal investigator of an ongoing project funded by the Government of India.
The present book is written based on author’s teaching experience of 50 years. He is the joint author ( with Avishek Adhikari) of another Springer book “Basic Modern Algebra with Applications”, 2014.
Bibliographic Information
Book Title: Basic Algebraic Topology and its Applications
Authors: Mahima Ranjan Adhikari
DOI: https://doi.org/10.1007/978-81-322-2843-1
Publisher: Springer New Delhi
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer India 2016
Hardcover ISBN: 978-81-322-2841-7Published: 26 September 2016
Softcover ISBN: 978-81-322-3855-3Published: 15 June 2018
eBook ISBN: 978-81-322-2843-1Published: 16 September 2016
Edition Number: 1
Number of Pages: XXIX, 615
Number of Illustrations: 176 b/w illustrations
Topics: Algebraic Topology, Topological Groups, Lie Groups, Manifolds and Cell Complexes (incl. Diff.Topology), Group Theory and Generalizations, K-Theory