KnowraHomotopy equivalenceLinked fromLinked fromThe 9 pages that link to Homotopy equivalence, each with the reason it gives.All 9Broader topic 3Related 2Compared with 4Equivalence relationRelated: It groups spaces by their large-scale topological shape rather than exact form.Fundamental groupRelated: Homotopy-equivalent spaces have isomorphic fundamental groups.HomeomorphismCompared with: It is weaker than homeomorphism: spaces can be homotopy equivalent without being homeomorphic.Algebraic topologyCompared with: It defines a coarser notion of sameness than homeomorphism, the usual target of homotopy invariants.IsomorphismCompared with: It can identify spaces up to continuous deformation without requiring a homeomorphism.HomotopyBroader topic: It uses homotopies to define when two spaces have the same homotopy type.Whitehead theoremBroader topic: This is the stronger conclusion guaranteed for the specified spaces.Excision theoremCompared with: It gives homology isomorphisms by comparing whole spaces up to deformation.Generalized Poincaré conjectureBroader topic: The hypothesis asks a manifold to have the sphere’s homotopy type, not merely its homology.