- kernels. A
cochain complex is
similar to a
chain complex,
except that its
homomorphisms are in the
opposite direction. The
homology of a
cochain complex...
-
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...
- 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...
- 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 )...
-
starts with a
product of
cochains: if αp{\displaystyle \alpha ^{p}} is a p-
cochain and βq{\displaystyle \beta ^{q}} is a q-
cochain, then (αp⌣βq)(σ)=αp(σ∘ι0...
- {\displaystyle {\mathcal {F}}(|\sigma |)} , and we
denote the set of all q-
cochains of U {\displaystyle {\mathcal {U}}} with
coefficients in F {\displaystyle...
- {\displaystyle C^{\bullet }(X)} ) is the
complex of its
cellular chains (or
cochains, respectively).
Consider then the
composition C ∙ ( X ) ⊗ C ∙ ( X ) ⟶ Δ...
-
gives a
linear map from the
space of k-forms to the kth
group of
singular cochains, Ck(M, Z), the
linear functionals on Ck(M, Z). In
other words, a k-form...
