List of algebraic topology topics

Table of contents

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

Homology (mathematics)

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

• Homotopy
• Fundamental group
• Simply connected
  • Universal cover
• Fibre bundle
  • Möbius strip
  • Vector bundle
  • Fibration

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

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