- 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...
-
usually one ****ociated with a
topological space,
often defined from a
cochain complex.
Cohomology can be
viewed as a
method of ****igning
richer algebraic...
-
whole interval which makes the
difference quotient a 1 {\displaystyle 1} -
cochain. The most
common notation for the
difference quotient is: Δ f Δ x ( x +...
- {F}})} is an
abelian group by
pointwise addition. The
cochain groups can be made into a
cochain complex ( C ∙ ( U , F ) , δ ) {\displaystyle (C^{\bullet...
-
homology is an
oriented link
invariant that
arises as the
cohomology of a
cochain complex. It may be
regarded as a
categorification of the
Jones polynomial...
- 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 ∙ ) ...
- In
mathematics a
cocycle is a
closed cochain.
Cocycles are used in
algebraic topology to
express obstructions (for example, to
integrating a differential...
- 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 )...
- {g}},M)} are
called cochains from g {\displaystyle {\mathfrak {g}}} to M {\displaystyle M} . A
homogeneous n {\displaystyle n} -
cochain from g {\displaystyle...
- po****r mathematics.)
There is also a
related notion of the
cohomology of a
cochain complex,
giving rise to
various cohomology theories, in
addition to the...
