List of algebraic topology topics

From Wikinfo

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

Contents 1 Homology (mathematics) 2 Homotopy theory 3 Further developments 4 Homological algebra 5 History 5.1 References

Homology (mathematics)

• Simplex
• Simplicial complex
  • Polytope
  • Triangulation
• Chain (mathematics)
• Betti number
• Euler characteristic
  • Genus
• 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
• Fibre bundle
  • [[M�bius strip]]
  • Line bundle
  • Vector bundle
  • Fibration

Further developments

• [[K�nneth theorem]]
• De Rham cohomology
• Characteristic class
  • Chern class
  • Chern-Simons form
  • Pontryagin class
• [[Poincar� 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

References

• Adapted from the Wikipedia article, "List_of_algebraic_topology_topics" http://en.wikipedia.org/wiki/List_of_algebraic_topology_topics, used under the GNU Free Documentation License