List of algebraic topology topics
This is a list of algebraic topology topics.
[Homology (mathematics)]
- Simplex
- Simplicial complex
- *Polytope
- *Triangulation
- *Barycentric subdivision
- *Simplicial approximation theorem
- *Abstract simplicial complex
- *Simplicial set
- *Simplicial category
- Chain (algebraic topology)
- Betti number
- Euler characteristic
- *Genus
- *Riemann–Hurwitz formula
- Singular homology
- Cellular homology
- Relative homology
- Mayer–Vietoris sequence
- Excision theorem
- Universal coefficient theorem
- Cohomology
- *List of cohomology theories
- *Cocycle class
- *Cup product
- *Cohomology ring
- *De Rham cohomology
- *Čech cohomology
- *Alexander–Spanier cohomology
- *Intersection cohomology
- *Lusternik–Schnirelmann category
- Poincaré duality
- Fundamental class
- Applications
- *Jordan curve theorem
- *Brouwer fixed point theorem
- *Invariance of domain
- *Lefschetz fixed-point theorem
- *Hairy ball theorem
- *Degree of a continuous mapping
- *Borsuk–Ulam theorem
- *Ham sandwich theorem
- *Homology sphere
Homotopy theory
- Homotopy
- Path (topology)
- Fundamental group
- Homotopy group
- Seifert–van Kampen theorem
- Pointed space
- Winding number
- Simply connected
- *Universal cover
- Monodromy
- Homotopy lifting property
- Mapping cylinder
- Mapping cone (topology)
- Wedge sum
- Smash product
- Adjunction space
- Cohomotopy
- Cohomotopy group
- Brown's representability theorem
- Eilenberg–MacLane space
- Fibre bundle
- *Möbius strip
- *Line bundle
- **Canonical line bundle
- *Vector bundle
- *Associated bundle
- *Fibration
- *Hopf bundle
- *Classifying space
- Cofibration
- Homotopy groups of spheres
- Plus construction
- Whitehead theorem
- Weak equivalence
- Hurewicz theorem
- H-space
Further developments
- Künneth theorem
- De Rham cohomology
- Obstruction theory
- Characteristic class
- *Chern class
- *Chern–Simons form
- *Pontryagin class
- *Pontryagin number
- *Stiefel–Whitney class
- Poincaré conjecture
- Cohomology operation
- *Steenrod algebra
- Bott periodicity theorem
- K-theory
- *Topological K-theory
- *Adams operation
- *Algebraic K-theory
- *Whitehead torsion
- *Twisted K-theory
- Cobordism
- Thom space
- Suspension functor
- Stable homotopy theory
- Spectrum (homotopy theory)
- Morava K-theory
- Hodge conjecture
- Weil conjectures
- Directed algebraic topology
Applied topology
Example: DE-9IM[Homological algebra]
- Chain complex
- Commutative diagram
- Exact sequence
- *Five lemma
- *Short five lemma
- *Snake lemma
- *Splitting lemma
- *Extension problem
- Spectral sequence
- Abelian category
- Group cohomology
- Sheaf
- *Sheaf cohomology
- *Grothendieck topology
- Derived category