Basic Algebraic Topology and its Applications [electronic resource] by Mahima Ranjan Adhikari.

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 ch...

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Bibliographic Details
Main Author: Adhikari, Mahima Ranjan (Author)
Corporate Author: SpringerLink (Online service)
Language:English
Published: New Delhi : Springer India : Imprint: Springer, 2016.
Edition:1st ed. 2016.
Subjects:
Algebraic topology.
Topological groups.
Lie groups.
Manifolds (Mathematics).
Group theory.
K-theory.
Online Access:
Springer Mathematics and Statistics eBooks 2016 English/International: 2016 (Springer Link)
Format: Electronic eBook
Contents:
  • Prerequisite Concepts and Notations
  • Basic Homotopy
  • The Fundamental Groups.-Covering Spaces
  • Fibre Bundles, Vector Bundles and K-theory
  • Geometry of Simplicial Complexes and Fundamental Groups
  • Higher Homotopy Groups
  • Products in Higher Homotopy Groups
  • CW-complexes and Homotopy
  • Eilenberg-MacLane Spaces
  • Homology and Cohomology Theories
  • Eilenberg-Steenrod Axioms for Homology and Cohomology Theories
  • Consequences of the Eilenberg-Steenrod Axioms
  • Some Applications of Homology Theory
  • Spectral Homology and Cohomology Theories
  • Obstruction Theory
  • More Relations Between Homotopy and Homology Groups
  • A Brief Historical Note.