Definition of Cocycles. Meaning of Cocycles. Synonyms of Cocycles

Here you will find one or more explanations in English for the word Cocycles. Also in the bottom left of the page several parts of wikipedia pages related to the word Cocycles and, of course, Cocycles synonyms and on the right images related to the word Cocycles.

Definition of Cocycles

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Meaning of Cocycles from wikipedia

- 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...
- an intrinsic way. The other vector bundles of tensors have comparable cocycles, which come from applying functorial properties of tensor constructions...
- 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,...
- 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...
- 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...
- 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...
- 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...