Advertisement

Basic Algebraic Topology and its Applications

  • Mahima Ranjan Adhikari

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Mahima Ranjan Adhikari
    Pages 1-44
  3. Mahima Ranjan Adhikari
    Pages 45-106
  4. Mahima Ranjan Adhikari
    Pages 107-145
  5. Mahima Ranjan Adhikari
    Pages 147-196
  6. Mahima Ranjan Adhikari
    Pages 197-247
  7. Mahima Ranjan Adhikari
    Pages 273-304
  8. Mahima Ranjan Adhikari
    Pages 305-327
  9. Mahima Ranjan Adhikari
    Pages 329-346
  10. Mahima Ranjan Adhikari
    Pages 347-406
  11. Mahima Ranjan Adhikari
    Pages 407-417
  12. Mahima Ranjan Adhikari
    Pages 433-443
  13. Mahima Ranjan Adhikari
    Pages 445-473
  14. Mahima Ranjan Adhikari
    Pages 475-509
  15. Mahima Ranjan Adhikari
    Pages 511-531
  16. Mahima Ranjan Adhikari
    Pages 533-545
  17. Mahima Ranjan Adhikari
    Pages 547-568
  18. Back Matter
    Pages 569-615

About this book

Introduction

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.

Keywords

Homotopy and cohomotopy group Vector bundle Homology and cohomology group Eilenberg-Steenrod axioms Spectrum of spaces Generalized cohomology Cohomology operations Hopf invariant and Knot group

Authors and affiliations

  • Mahima Ranjan Adhikari
    • 1
  1. 1.Bioinformatics, Information TechnolThe Institute for MathematicsKolkataIndia

Bibliographic information