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Algebraic Topology

Algebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminarie...

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Bibliographic Details
Main Authors: Bray, Clark, Butscher, Adrian (Author), Rubinstein-Salzedo, Simon (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2021, 2021
Edition:1st ed. 2021
Subjects:
Group Theory
Topological Groups, Lie Groups
Lie Groups
Topological Groups
Algebraic Topology
Group Theory And Generalizations
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Introduction
  • 1. Surface Preliminaries
  • 2. Surfaces
  • 3. The Euler Characteristic and Identification Spaces
  • 4. Classification Theorem of Compact Surfaces
  • 5. Introduction to Group Theory
  • 6. Structure of Groups
  • 7. Cosets, Normal Subgroups, and Quotient Groups
  • 8. The Fundamental Group
  • 9. Computing the Fundamental Group
  • 10. Tools for Fundamental Groups
  • 11. Applications of Fundamental Groups
  • 12. The Seifert-Van Kampen Theorem
  • 13. Introduction to Homology
  • 14. The Mayer-Vietoris Sequence
  • A. Topological Notions
  • Bibliography
  • Index

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