- In
mathematics a
cocycle is a
closed cochain.
Cocycles are used in
algebraic topology to
express obstructions (for example, to
integrating a differential...
- 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...
- 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...
- 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...
- an
intrinsic way. The
other vector bundles of
tensors have
comparable cocycles,
which come from
applying functorial properties of
tensor constructions...
- 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,...
- 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...
- }
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...
-
corresponds to the
group 1-
cocycle φ 0 ( f ) = log f ′ . {\displaystyle \varphi _{0}(f)=\log f'.} The
corresponding Lie
algebra 1-
cocycles for λ = 0, 1, 2 are...
