Basic Algebraic Topology and its Applications

• Κύριος συγγραφέας: Adhikari, Mahima Ranjan (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New Delhi : Springer India : Imprint: Springer, 2016.
• Θέματα: Mathematics.; Group theory.; K-theory.; Topological groups.; Lie groups.; Algebraic topology.; Manifolds (Mathematics).; Complex manifolds.; Algebraic Topology.; Topological Groups, Lie Groups.; Manifolds and Cell Complexes (incl. Diff.Topology).; Group Theory and Generalizations.; K-Theory.

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...

Πίνακας περιεχομένων:

• 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.