In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential equation on a closed manifold). They are likewise used in group cohomology. In autonomous dynamical systems, cocycles are used to describe particular kinds of map, as in Oseledets theorem.

Definition

Algebraic Topology

Let X be a CW complex be the singular cochains are cocycles are coboundaries, which means cocycles vanish on boundaries.

See also

• Čech cohomology

• Cocycle condition

References