# Poincaré space

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**Poincaré space** (*plural* **Poincaré spaces**)

- (topology) An
*n*-dimensional topological space with a distinguished element*µ*of its*n*th homology group such that taking the cap product with an element of the*k*th cohomology group yields an isomorphism to the (*n*−*k*)th cohomology group.*Any closed, orientable, connected manifold is a***Poincaré space**.