From Surf Wiki (app.surf) — the open knowledge base

Poincaré space

Quality 0.00 · 0 views · Updated 7 days ago

In algebraic topology, a Poincaré space is an n-dimensional topological space with a distinguished element μ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th homology group. The space is essentially one for which Poincaré duality is valid; more precisely, one whose singular chain complex forms a Poincaré complex with respect to the distinguished element μ.