Homotopy type

Summary

Two topological spaces have the same homotopy type when there is a homotopy equivalence between them. The homotopy type of a space is its class under this equivalence relation. Most invariants of algebraic topology, such as homotopy groups, homology and cohomology, depend only on the homotopy type. Classifying spaces up to homotopy type is a central aim of homotopy theory.