algebraic topology

noun1

1. •
   The branch of mathematics that uses tools from abstract algebra to study topological spaces.

   • The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).
   • Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.