Poincaré space

noun

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.”

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Meanings

nounPoincaré space (plural Poincaré spaces)

plural Poincaré spaces

  1. mathematicsAn 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.

Cite this entry
APA

Poincaré space. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Poincar%C3%A9%20space

MLA

“Poincaré space.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Poincar%C3%A9%20space. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Poincaré space,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Poincar%C3%A9%20space.

Source: Poincaré space on Wiktionary, CC BY-SA 4.0.