-
singular cochains is only graded-commutative up to
chain homotopy. In fact, it is
impossible to
modify the
definition of
singular cochains with coefficients...
-
homology and
cohomology theory including chain and
cochain complexes, the cup
product H****ler Whitney:
cochains as
integrands The
recent development of discrete...
- exact. A
cochain complex is
similar to a
chain complex,
except that its
homomorphisms are in the
opposite direction. The
homology of a
cochain complex...
- This is an
abelian group; its
elements are
called the (inhomogeneous) n-
cochains. The
coboundary homomorphisms are
defined by { d n + 1 : C n ( G , M )...
- {\displaystyle {\mathcal {F}}(|\sigma |)} , and we
denote the set of all q-
cochains of U {\displaystyle {\mathcal {U}}} with
coefficients in F {\displaystyle...
- de Rham
cohomology of the manifold. In
algebraic topology, the
singular cochains of a
topological space form a DGA
encoding the
singular cohomology. Moreover...
- of
abelian groups defined from a
cochain complex. That is,
cohomology is
defined as the
abstract study of
cochains, cocycles, and coboundaries. Cohomology...
- be a CW
complex and C n ( X ) {\displaystyle C^{n}(X)} be the
singular cochains with
coboundary map d n : C n − 1 ( X ) → C n ( X ) {\displaystyle d^{n}:C^{n-1}(X)\to...
- quasi-isomorphism or
quism is a
morphism A → B of
chain complexes (respectively,
cochain complexes) such that the
induced morphisms H n ( A ∙ ) → H n ( B ∙ ) ...
- {g}},M)} are
called cochains from g {\displaystyle {\mathfrak {g}}} to M {\displaystyle M} . A
homogeneous n {\displaystyle n} -
cochain from g {\displaystyle...
