Английская Википедия:Cocycle
Шаблон:One source 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 the Oseledets theorem.[1]
Definition
Algebraic Topology
Let X be a CW complex and <math>C^n(X)</math> be the singular cochains with coboundary map <math>d^n: C^{n-1}(X) \to C^n(X)</math>. Then elements of <math>\text{ker }d</math> are cocycles. Elements of <math> \text{im } d </math> are coboundaries. If <math> \varphi</math> is a cocycle, then <math>d \circ \varphi = \varphi \circ \partial =0 </math>, which means cocycles vanish on boundaries. [2]
See also
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