algebraic topology, homological connectivity is a property describing a topological space based on its homology groups. X is homologically-connected if its...

theorem, G has an ISR. One family of conditions is based on the homological connectivity of the independence complex of subgraphs. To state the conditions...

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

related to the homological connectivity of the independence complex of a graph, which is the smallest index k such that all reduced homological groups up to...

Look up connectivity in Wiktionary, the free dictionary. Connectivity may refer to: Connectivity (media), the ability of the social media to accumulate...

is true for Hi(S) for all i not equal to 0 or 1. Therefore, the homological connectivity of the triangle is 0 (it is the largest k for which the reduced...

Extraordinary homology theory Homological algebra Homological conjectures in commutative algebra Homological connectivity Homological dimension Homotopy group...

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

a graph G, that can be used to calculate a lower bound on the homological connectivity of the independence complex of G. The matching complex of a graph...

_{y\in Y_{0}}V_{y}.} Suppose that, for every subset Y0 of Y, the homological connectivity plus 2 of the sub-complex induced by V Y 0 {\displaystyle V_{Y_{0}}}...

deeper aspects of commutative rings have been studied using methods from homological algebra. Hochster (2007) lists some open questions in this area of active...

In the branch of mathematics called homological algebra, a t-structure is a way to axiomatize the properties of an abelian subcategory of a derived category...

what is now called stable homotopy theory. It is a reformulation using homological algebra, and an extension, of a technique called 'killing homotopy groups'...

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

study of geometric objects using homological algebra and homotopy. Since objects in this field should encode the homological and homotopy information, there...

constructing the Adams spectral sequence. Essentially, the idea is to take a connective spectrum of finite type X {\displaystyle X} and iteratively resolve with...

there is no glossary of homological algebra in Wikipedia right now, this glossary also includes a few concepts in homological algebra (e.g., chain homotopy);...

dynamical systems is to relate their structural properties (e.g. the network connectivity) and the global dynamics that result. Projected dynamical systems is...

35 (4): 257–285. doi:10.1007/BF02760652. Barbara L. Osofsky (1968). "Homological dimension and the continuum hypothesis" (PDF). Transactions of the American...

mathematics of the twentieth century, in particular in subjects based around homological algebra. The explication of the particular axioms used in a theory can...

Eilenberg (1956) Provided the first fully worked out treatment of abstract homological algebra, unifying previously disparate presentations of homology and...

S2CID 250889913. Kontsevich, Maxim; Soibelman, Yan (7 November 2000). "Homological mirror symmetry and torus fibrations". arXiv:math/0011041. Mikhalkin...

elegantly defined and characterized sheaf cohomology in the language of homological algebra. The essential point is to fix the space X and think of sheaf...