List of algebraic topology topics
Algebraic topology uses abstract algebra to study topological spaces
From Wikipedia, the free encyclopedia
This is a list of algebraic topology topics.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.
Homology (mathematics)
Homotopy theory
- Homotopy
- Path (topology)
- Fundamental group
- Homotopy group
- Seifert–van Kampen theorem
- Pointed space
- Winding number
- Simply connected
- 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
- 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
- Poincaré conjecture
- Cohomology operation
- Bott periodicity theorem
- 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