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Definition of Poincaré space
1. Noun. (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. ¹
¹ Source: wiktionary.com