﻿

# Cocycle

A cocycle refers to any one of the following:

Let G be a graph with vertex set V. A cut is a partition S = {X, X'} of V into two nonempty subsets. We denote the set of all edges incident with one vertex in X and one vertex in X' by E(S) or E(X, X'); and any such edge set is called a cocycle. [pg 103 ISBN 1431-1550]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• cocycle — noun A cochain that is in the kernel of a coboundary map …   Wiktionary

• Cocycle class — In mathematics, more specifically in cohomology theory, a cocycle in the cochain group is associated with a unique equivalence class known as the cocycle class or coclass of …   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

• 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

• Čech cohomology — In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Contents 1 Motivation 2… …   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

• Oseledets theorem — In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a nonlinear dynamical system. It was proved by Valery Oseledets (also spelled Oseledec ) in 1965 …   Wikipedia

• GRAPHES (THÉORIE DES) — On appelle théorie des graphes une classe de problèmes plus ou moins bien résolus. Leur résolution suscite chez les mathématiciens, en particulier à l’étranger, un engouement sans cesse croissant. Claude Berge, dans le discours inaugural des… …   Encyclopédie Universelle

• Random dynamical system — In mathematics, a random dynamical system is a measure theoretic formulation of a dynamical system with an element of randomness , such as the dynamics of solutions to a stochastic differential equation. It consists of a base flow, the noise ,… …   Wikipedia

• Tensor field — In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of… …   Wikipedia