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Basic Algebraic Topology and its Applications

Authors: Adhikari, Mahima Ranjan

  • 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
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eBook $69.99
price for USA (gross)
  • ISBN 978-81-322-2843-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-81-322-2841-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Mahima Ranjan Adhikari, PhD, is a former professor of Pure Mathematics at the University of Calcutta. His main interest lies in algebra and topology. He has published a number of papers in several international journals including the Proceedings of American Mathematical Society and five textbooks. Eleven students have already been awarded the PhD degree under his supervision. He is a member of the American Mathematical Society and serves on the editorial board of several journals and research monographs. He was the president of the mathematical science section of the 95th Indian Science Congress, 2008.
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.

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)


Table of contents (18 chapters)

  • Prerequisite Concepts and Notations

    Adhikari, Mahima Ranjan

    Pages 1-44

  • Homotopy Theory: Elementary Basic Concepts

    Adhikari, Mahima Ranjan

    Pages 45-106

  • The Fundamental Groups

    Adhikari, Mahima Ranjan

    Pages 107-145

  • Covering Spaces

    Adhikari, Mahima Ranjan

    Pages 147-196

  • Fiber Bundles, Vector Bundles and K-Theory

    Adhikari, Mahima Ranjan

    Pages 197-247

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-81-322-2843-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-81-322-2841-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Basic Algebraic Topology and its Applications
Authors
Copyright
2016
Publisher
Springer India
Copyright Holder
Springer India
eBook ISBN
978-81-322-2843-1
DOI
10.1007/978-81-322-2843-1
Hardcover ISBN
978-81-322-2841-7
Edition Number
1
Number of Pages
XXIX, 615
Number of Illustrations and Tables
176 b/w illustrations
Topics