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

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...

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...

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

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....

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...

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}...

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

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

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

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...

{\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...

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

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

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...

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...

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

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

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...

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...

since eukaryotes may be part of the archaean clade and have multiple homologies with other Archaea. Prokaryotic cells are generally smaller and similar...

"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...

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...

activity and inheritance, with emphasis on widespread homology effects, phenomena in which homology between chromosomes plays a role. Her studies have explored...

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...

p53, also known as tumor protein p53, TP53, cellular tumor antigen p53 (UniProt name), or transformation-related protein 53 (TRP53) is a regulatory transcription...

Proline-rich protein 23C is a protein that in humans is encoded by the proline-rich 23C (PRR23C) gene. PRR23C Homo sapiens is located on the long arm of...

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...