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 rational homology sphere is a topological space which need not be homeomorphic to an n-sphere, but which has the same rational homology as an $n$-sphere.
Every homology sphere is a rational homology sphere.
The Wu manifold $W=SU(3)/SO(3)$ is a simply connected rational homology $5$-sphere (with non-trivial homology groups $H_0(W)\cong\mathbb{Z}$, $H_2(W)\cong\mathbb{Z}_2$ and $H_5(W)\cong\mathbb{Z}$), but isnβt a homotopy $5$-sphere.
Last revised on May 31, 2024 at 15:04:15. See the history of this page for a list of all contributions to it.