homotopical connectivity is a property describing a topological space based on the dimension of its holes. In general, low homotopical connectivity indicates...
19 KB (3,209 words) - 01:06, 16 October 2023
Homotopical connectivity, a property related to the dimensions of holes in a topological space, and to its homotopy groups. Homological connectivity,...
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biology, homotopic connectivity is the connectivity between mirror areas of the human brain hemispheres. Changes in the homotopic connectivity occur in...
2 KB (263 words) - 17:47, 17 April 2024
Homotopical connectivity. Meshulam's game is a game played on a graph G, that can be used to calculate a lower bound on the homological connectivity of...
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Join (topology) (section Homotopical connectivity)
{\displaystyle A,B} , the homotopical connectivity ( η π {\displaystyle \eta _{\pi }} ) of their join is at least the sum of connectivities of its parts:: 81...
16 KB (3,105 words) - 05:17, 16 May 2024
This implies, in particular, that the homological connectivity equals the homotopical connectivity when the latter is at least 1. In addition, the Hurewicz...
9 KB (1,309 words) - 00:36, 19 August 2023
_{m,n}} is min ( m , n ) − 1 {\displaystyle \min(m,n)-1} . The homotopical connectivity of the chessboard complex is at least min ( m , n , m + n + 1 3...
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Derived algebraic geometry (redirect from Homotopical algebraic geometry)
{\displaystyle A_{i}} Moreover, the spectral scheme X {\displaystyle X} is called connective if π i ( O X ) = 0 {\displaystyle \pi _{i}({\mathcal {O}}_{\mathfrak {X}})=0}...
14 KB (1,810 words) - 16:44, 31 July 2024
extra that is not needed. Merker, for instance, argues that the homotopic connectivity of sensory pathways does the necessary work. In modern connectionism...
51 KB (6,484 words) - 19:49, 21 August 2024
JSTOR 1969744. MR 0058971. Brown, Ronald; Loday, Jean-Louis (1987). "Homotopical excision, and Hurewicz theorems, for n-cubes of spaces". Proceedings...
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including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories, including algebraic topology, categorical...
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whose 0-skeleton consists of a single point. Consider climbing up the connectivity ladder—assume X is a simply-connected CW complex whose 0-skeleton consists...
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is contractible in X. Semi-local simple connectivity, a strictly weaker condition than local simple connectivity, is a necessary condition for the existence...
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functor from topological spaces to abelian groups (or R-modules). Two homotopic maps from X to Y induce the same homomorphism on cohomology (just as on...
43 KB (6,691 words) - 21:02, 23 March 2024
proofs are elements of inhabited types is generalized to the notion of homotopic equivalence of proofs (as paths in space, the identity type or equality...
56 KB (6,174 words) - 01:56, 21 August 2024
it coincides with the union of the interiors of the polygons Pn. By connectivity, the tessellation must cover the whole of the upper half plane. To see...
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cellular approximation theorem says that every map between CW complexes is homotopic to a cellular map between them. 3. The cellular homology is the (canonical)...
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no. 1, 61–82. Beligiannis, Apostolos; Reiten, Idun. Homological and homotopical aspects of torsion theories. Mem. Amer. Math. Soc. 188 (2007), no. 883...
32 KB (6,305 words) - 09:49, 7 February 2024
du\wedge \star du>0,} contradicting the orthogonality condition on U. Connectivity and level curves. (1) A level curve for V divide X into two open connected...
38 KB (5,224 words) - 01:14, 26 June 2024