Algebraic topology

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.

Not to be confused with

For the topology of pointwise convergence, see Algebraic topology (object).

See also

• Algebraic K-theory
• Exact sequence
• Glossary of algebraic topology
• Grothendieck topology
• Higher category theory
• Higher-dimensional algebra
• Homological algebra
• K-theory
• Lie algebroid
• Lie groupoid
• Important publications in algebraic topology
• Serre spectral sequence
• Sheaf (mathematics)
• Topological quantum field theory
• Topological space

External links

• Algebraic topology @ Wikipedia.org