Word.ws English Dictionary

Poincaré space

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.

Noun

Poincaré space (plural Poincaré spaces)

  1. 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.

Forms of Poincaré space

pluralPoincaré spaces

Questions about Poincaré space

What does Poincaré space mean?
Poincaré space means 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.
What part of speech is Poincaré space?
Poincaré space is a noun.
What is the plural of Poincaré space?
The plural of Poincaré space is Poincaré spaces.

Words near Poincaré space in the dictionary

  1. Poincaré disks
  2. Poincaré map
  3. Poincaré maps
  4. Poincaré recurrence time
  5. Poincaré recurrence times
  6. Poincaré space
  7. Poincaré spaces
  8. Poincaré-Birkhoff-Witt theorem
  9. Poincaréan
  10. Poincarés
  11. poinciana

Source and license

Adapted from Wiktionary: Poincaré space (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “Poincaré space.” Word.ws, https://word.ws/poincar%C3%A9_space. Based on Wiktionary, CC BY-SA 4.0.