quaternionic projective line$\,\mathbb{H}P^1$
homotopy theory, (β,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directedβ¦
models: topological, simplicial, localic, β¦
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 homotopy sphere is a rational homotopy sphere.
Every homotopy sphere is a homology sphere.
Every simply connected homology sphere is a homotopy sphere.
A path-connected, $n$-connected, orientable and closed $2n$-manifold is a homotopy-$2n$-sphere.
A path-connected, $n$-connected, orientable and closed $2n+1$-manifold is a homotopy-$2n+1$-sphere.
Every smooth manifold homotopy-4-sphere is homeomorphic to the actual 4-sphere.
(due to Michael Freedman, see Siebenmann)
Last revised on March 21, 2024 at 16:32:47. See the history of this page for a list of all contributions to it.