mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide...

singular homology is referred to as ordinary homology. Derived category Excision theorem Hurewicz theorem Simplicial homology Cellular homology Hatcher...

Borel–Moore homology Cellular homology Cyclic homology Hochschild homology Floer homology Intersection homology K-homology Khovanov homology Morse homology Persistent...

CW complexes and cellular maps, cellular homology can be interpreted as a homology theory. To compute an extraordinary (co)homology theory for a CW complex...

homology; but if X and Y happen to be CW complexes, then this can be replaced by cellular homology, because that is isomorphic to singular homology....

characteristic Genus Riemann–Hurwitz formula Singular homology Cellular homology Relative homology Mayer–Vietoris sequence Excision theorem Universal coefficient...

In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of...

CW-complexes can be used to define cellular homology and one can show that cellular homology and simplicial homology coincide. For computational issues...

index γ . {\displaystyle \gamma .} Also by cellular homology, the rank of the n {\displaystyle n} th homology group of a CW complex M {\displaystyle M}...

currents. The isomorphism with singular homology can also be proved by demonstrating an isomorphism with cellular homology, by viewing an unstable manifold associated...

(so-called algebraic cycles) in a similar way to how simplicial or cellular homology groups are formed out of subcomplexes. When the variety is smooth...

{\displaystyle C_{i}M\to C^{\,n-i}M} , where C i {\displaystyle C_{i}} is the cellular homology of the triangulation T {\displaystyle T} , and C n − i M {\displaystyle...

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated...

Molecular & Cellular Proteomics. 12 (5): 1204–13. doi:10.1074/mcp.M112.025858. PMC 3650332. PMID 23358503. Sawyer TK (1998). "Src-homology 2 domains: Structure...

of a CW complex determines the natural homology, the cellular homology and that can be taken to be the homology of the complex.) A map f : A → X {\displaystyle...

regulated mechanism. It allows the orderly degradation and recycling of cellular components. Although initially characterized as a primordial degradation...

extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories...

holes, of a topological space. In algebraic topology and abstract algebra, homology (in part from Greek ὁμός homos "identical") is a certain general procedure...

Pleckstrin homology domain (PH domain) or (PHIP) is a protein domain of approximately 120 amino acids that occurs in a wide range of proteins involved...

observation. The most successful type of structure prediction, known as homology modeling, relies on the existence of a "template" structure with sequence...

_{\mathbf {a} }({\mathcal {V}}),} which is used when considering cellular homology instead of the Chow ring. The latter are disjoint affine spaces, of...

Homology-directed repair (HDR) is a mechanism in cells to repair double-strand DNA lesions. The most common form of HDR is homologous recombination. The...

between CW complexes is homotopic to a cellular map between them. 3.  The cellular homology is the (canonical) homology of a CW complex. Note it applies to...

proper. As in algebraic topology, there is a dual theory called group homology. The techniques of group cohomology can also be extended to the case that...

Pleckstrin homology domain containing A4 is a protein that in humans is encoded by the PLEKHA4 gene. This gene encodes a pleckstrin homology (PH) domain-containing...

Whereas homology-based methods can often be used to identify molecular functions of a protein, context-based approaches can be used to predict cellular function...

"shape". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data...

share one or more of the four characteristic domains of homology entitled the Bcl-2 homology (BH) domains (named BH1, BH2, BH3 and BH4), and can form...

necrosis, which is a form of traumatic cell death that results from acute cellular injury, apoptosis is a highly regulated and controlled process that confers...

signaling pathways interact with one another they form networks, which allow cellular responses to be coordinated, often by combinatorial signaling events. At...