Cocycle class

In mathematics, more specifically in cohomology theory, a $q \, \!$-cocycle $\alpha \, \!$ in the cochain group $S^q(X) \, \!$ is associated with a unique equivalence class $[\alpha] \in H^q(X) \, \!$ known as the cocycle class or coclass of $\alpha. \, \!$

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This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Homology theory Algebraic topology Algebra stubs Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Liberal League Smithland Look at other dictionaries: Class automorphism — In mathematics, in the realm of group theory, a class automorphism is an automorphism of a group that sends each element to within its conjugacy class. The class automorphisms form a subgroup of the automorphism group. Some facts: Every inner… …   Wikipedia JLO cocycle — In noncommutative geometry, the JLO cocycle is a cocycle (and thus defines a cohomology class) in entire cyclic cohomology. It is a non commutative version of the classic Chern character of the conventional differential geometry. In… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia List of algebraic topology topics — This is a list of algebraic topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of geometric topology topics Publications in topology Topological property Contents 1… …   Wikipedia System of imprimitivity — The concept of system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations. It was used by George Mackey as the basis for his theory of induced unitary… …   Wikipedia Orbifold — This terminology should not be blamed on me. It was obtained by a democratic process in my course of 1976 77. An orbifold is something with many folds; unfortunately, the word “manifold” already has a different definition. I tried “foldamani”,… …   Wikipedia Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia Fiber bundle — In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which looks locally like a product space. It may have a different global topological structure in that the space as a whole may not be homeomorphic to a… …   Wikipedia Projective representation — In the mathematical field of representation theory, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to :PGL( V ,F) = GL( V ,F)/F lowast; where GL( V ,F) is the automorphism group of… …   Wikipedia Cup product — In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”