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.
be the singular cochains with coboundary map
, which means cocycles vanish on boundaries.
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