Loading AI tools
Closed cochain From Wikipedia, the free encyclopedia
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.[1]
This article relies largely or entirely on a single source. (October 2022) |
Let X be a CW complex and be the singular cochains with coboundary map . Then elements of are cocycles. Elements of are coboundaries. If is a cocycle, then , which means cocycles vanish on boundaries. [2]