List of algebraic topology topics

This is a list of algebraic topology topics, by Wikipedia page.

Table of contents

1 Homology (mathematics) 2 Homotopy theory 3 Further developments 4 Homological algebra 5 History

Homology (mathematics)

Main article:Homology theory

• Simplex
• Simplicial complex
  • Polytope
  • Triangulation
• Chain (mathematics)
• Betti number
• Euler characteristic
  • Genus
• Singular homology
• Mayer-Vietoris sequence
• Applications
  • Jordan curve theorem
  • Brouwer fixed point theorem
  • Invariance of domain
  • Borsuk-Ulam Theorem

Homotopy theory

• Homotopy
• Fundamental group
• Seifert-van Kampen theorem
• Simply connected
  • Universal cover
• Monodromy
• Fibre bundle
  • Möbius strip
  • Line bundle
  • Vector bundle
  • Associated bundle
  • Fibration

Further developments

• Künneth theorem
• De Rham cohomology
• Characteristic class
  • Chern class
  • Chern-Simons form
  • Pontryagin class
• Poincaré conjecture
• K-theory
• Cobordism
• Hodge conjecture
• Weil conjectures

Homological algebra

• Chain complex
• Commutative diagram
• Exact sequence
  • Five lemma
  • Short five lemma
  • Snake lemma
  • Splitting lemma
  • Extension problem
• Abelian category
• Group cohomology
• Sheaf
  • Grothendieck topology

History

• Combinatorial topology