Homotopy, Homology, Cohomology, and Covering Spaces

Algebraic-topology foundations: homotopy, fundamental groups, covering spaces, homology, cohomology, and characteristic-class background.

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Mathematics / Algebraic Topology / Homotopy, homology, and cohomology

Algebraic Topology notes
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Homology, Cohomology, and Characteristic Classes Homotopy and Covering Spaces Homotopy, Homology, Cohomology, and Covering Spaces

Reading Guide

This note collects the algebraic-topology background that later appears in characteristic classes and gauge examples: homotopy, fundamental groups, covering spaces, homology, cohomology, and the idea that global obstructions can be measured algebraically.

It is meant to explain why topology can produce integer-valued invariants, not to replace a full algebraic-topology text.

Shorter entry points now live beside this comprehensive version:

  • Homotopy and Covering Spaces
  • Homology, Cohomology, and Characteristic Classes