homotopical connectivity is a property describing a topological space based on the dimension of its holes. In general, low homotopical connectivity indicates...

Homotopical connectivity, a property related to the dimensions of holes in a topological space, and to its homotopy groups. Homological connectivity,...

biology, homotopic connectivity is the connectivity between mirror areas of the human brain hemispheres. Changes in the homotopic connectivity occur in...

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...

{\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...

This implies, in particular, that the homological connectivity equals the homotopical connectivity when the latter is at least 1. In addition, the Hurewicz...

_{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...

{\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}...

extra that is not needed. Merker, for instance, argues that the homotopic connectivity of sensory pathways does the necessary work. In modern connectionism...

JSTOR 1969744. MR 0058971. Brown, Ronald; Loday, Jean-Louis (1987). "Homotopical excision, and Hurewicz theorems, for n-cubes of spaces". Proceedings...

including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories, including algebraic topology, categorical...

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...

is contractible in X. Semi-local simple connectivity, a strictly weaker condition than local simple connectivity, is a necessary condition for the existence...

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...

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...

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...

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)...

no. 1, 61–82. Beligiannis, Apostolos; Reiten, Idun. Homological and homotopical aspects of torsion theories. Mem. Amer. Math. Soc. 188 (2007), no. 883...

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...