What does poincare space mean?
Definitions for poincare space
poin·care space
This dictionary definitions page includes all the possible meanings, example usage and translations of the word poincare space.
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Wiktionary
Poincaré spacenoun
An n-dimensional topological space with a distinguished element u00B5 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.
Wikipedia
Poincaré space
In algebraic topology, a Poincaré space is 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 homology group. The space is essentially one for which Poincaré duality is valid; more precisely, one whose singular chain complex forms a Poincaré complex with respect to the distinguished element µ. For example, any closed, orientable, connected manifold M is a Poincaré space, where the distinguished element is the fundamental class [ M ] . {\displaystyle [M].} Poincaré spaces are used in surgery theory to analyze and classify manifolds. Not every Poincaré space is a manifold, but the difference can be studied, first by having a normal map from a manifold, and then via obstruction theory.
Numerology
Chaldean Numerology
The numerical value of poincare space in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of poincare space in Pythagorean Numerology is: 8
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"poincare space." Definitions.net. STANDS4 LLC, 2024. Web. 27 May 2024. <https://www.definitions.net/definition/poincare+space>.
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