English Dictionary

Poincaré space

noun

(topology) 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 cohomology group.

The Poincaré space is a mathematical concept used in topology.

意味（1）

(topology) 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 cohomology group.

Any closed, orientable, connected manifold is a Poincaré space.