Definition of Cocycles. Meaning of Cocycles. Synonyms of Cocycles

- In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential...
- as 1-cocycles modulo an equivalence relation instead of by 1-coboundaries. The condition for a map φ {\displaystyle \varphi } to be a 1-cocycle is that...
- needed] The multiplicative ergodic theorem is stated in terms of matrix cocycles of a dynamical system. The theorem states conditions for the existence...
- In the complex case, the Neron-Severi group is therefore the group of 2-cocycles whose Poincaré dual is represented by a complex hypersurface, that is,...
- an intrinsic way. The other vector bundles of tensors have comparable cocycles, which come from applying functorial properties of tensor constructions...
- set of all q-cocycles. Thus a (q−1)-cochain f {\displaystyle f} is a cocycle if for all q-simplices σ {\displaystyle \sigma } the cocycle condition ∑ j...
- } Cocycles of the form c ( g , h ) = a g h a h a g h − 1 {\displaystyle c(g,h)=a_{g}^{h}a_{h}a_{gh}^{-1}} are called split. Cocycles under multiplication...
- In mathematics, the Teichmüller cocycle is a certain 3-cocycle ****ociated to a simple algebra A over a field L which is a finite Galois extension of a...
- topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an ****ociative (and...
- extension by a 2-cocycle. Below follows some results regarding central extensions and 2-cocycles. Theorem Let φ1 and φ2 be cohomologous 2-cocycles on a Lie algebra...