homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
A homotopy sphere is a topological space which need not be homeomorphic to an n-sphere, but which has the same homotopy type as an $n$-sphere.
Every smooth manifold homotopy-4-sphere is homeomorphic to the actual 4-sphere.
(due to Michael Freedman, see Siebenmann)
Last revised on December 1, 2019 at 14:12:35. See the history of this page for a list of all contributions to it.