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Algebraic topology [electronic resource] / Clark Bray, Adrian Butscher, Simon Rubinstein-Salzedo.

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
Online Access: Full Text (via Springer)
Main Authors: Bray, Clark (Author), Butscher, Adrian (Author), Rubinstein-Salzedo, Simon (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer, 2021.
Subjects:
Algebraic topology.
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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