Definition of Cocycle. Meaning of Cocycle. Synonyms of Cocycle

- In mathematics a cocycle is a closed cochain. Cocycles are used in algebraic topology to express obstructions (for example, to integrating a differential...
- 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...
- {\displaystyle M} . Then, these functions must also satisfy a cocycle condition, which gives a 1-cocycle on M {\displaystyle M} with values in its tangent bundle...
- needed] The multiplicative ergodic theorem is stated in terms of matrix cocycles of a dynamical system. The theorem states conditions for the existence...
- 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...
- satisfying certain condition (so-called cocycle condition). In fact, a factor system constitutes a realisation of the cocycles in the second cohomology group in...
- In category theory, a branch of mathematics, the cocycle category of objects X, Y in a model category is a category in which the objects are pairs of...
- is a method of adjoining two cocycles of degree p {\displaystyle p} and q {\displaystyle q} to form a composite cocycle of degree p + q {\displaystyle...
- from a 2-cocycle φ, it suffices to show that every 2-cocycle is a coboundary. Suppose φ is a 2-cocycle on g. The task is to use this 2-cocycle to manufacture...
- the kind of self-consistency the cocycle expresses. The construction of tensor densities is a 'twisting' at the cocycle level. Geometers have not been in...