simplicial chain
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Simplicial homology — In mathematics, in the area of algebraic topology, simplicial homology is a theory with a finitary definition, and is probably the most tangible variant of homology theory. Simplicial homology concerns topological spaces whose building blocks are … Wikipedia
Simplicial set — In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a well behaved topological space. Historically, this model arose from earlier work in combinatorial topology and… … Wikipedia
Simplicial complex — In mathematics, a simplicial complex is a topological space of a particular kind, constructed by gluing together points, line segments, triangles, and their n dimensional counterparts (see illustration). Simplicial complexes should not be… … Wikipedia
Chain complex — Bicomplex redirects here. For the number, see Bicomplex number In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between … Wikipedia
Chain (algebraic topology) — This article is about algebraic topology. For the term chain in order theory, see chain (order theory). In algebraic topology, a simplicial k chain is a formal linear combination of k simplices.[1] Integration on chains Integration is defined on… … Wikipedia
Polygonal chain — A simple polygonal chain A self intersecting polygonal chain … Wikipedia
Homology (mathematics) — In mathematics (especially algebraic topology and abstract algebra), homology (in Greek ὁμός homos identical ) is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a… … Wikipedia
Pushforward (homology) — Let X and Y be two topological spaces and f:X ightarrow Y a continuous function. Then f induces a homomorphism between the homology groups f {*}:H nleft(X ight) ightarrow H nleft(Y ight) for ngeq0. We say that f {*} is the pushforward induced by… … Wikipedia
Cycle — Contents 1 Chemistry 2 Economics 3 Mathematics 4 Music … Wikipedia
Simplex — For other uses, see Simplex (disambiguation). A regular 3 simplex or tetrahedron In geometry, a simplex (plural simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n… … Wikipedia
Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… … Wikipedia
