Cocycle

A cocycle refers to any one of the following:

• A closed cochain in algebraic topology is called a cocycle.
• A particular type of map in an autonomous dynamical system; see Oseledec theorem.

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.

There is also a meaning in group cohomology.

See also

• Čech cohomology

References

• Warner, Frank W. (1983). Foundations of Differentiable Manifolds and Lie Groups. New York: Springer. ISBN 0-387-90894-3.