- In mathematics, a
chain complex is an
algebraic structure that
consists of a
sequence of
abelian groups (or modules) and a
sequence of
homomorphisms between...
- {\mathcal {F}})} is the set of all q-
coboundaries. For example, a 1-cochain f {\displaystyle f} is a 1-
coboundary if
there exists a 0-cochain h {\displaystyle...
-
expository paper of
Savage (2009) for an
explanation of
symmetric and
coboundary monoidal categories, and the book by
Chari and
Pressley (1995) for ribbon...
- 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...
-
cocycles is
again a cocycle, and the
product of a
coboundary with a
cocycle (in
either order) is a
coboundary. The cup
product operation induces a bilinear...
-
differential of a
function on a
differentiable manifold Differential (
coboundary), in
homological algebra and
algebraic topology, one of the maps of a...
-
abelian group; its
elements are
called the (inhomogeneous) n-cochains. The
coboundary homomorphisms are
defined by { d n + 1 : C n ( G , M ) → C n + 1 ( G ...
-
derivative d has the
property that d2 = 0, it can be used as the
differential (
coboundary) to
define de Rham
cohomology on a manifold. The k-th de Rham cohomology...
- ∙ , d ∙ ) , {\displaystyle (C_{\bullet },d_{\bullet }),} the maps (or
coboundary operators) di are
often called differentials. Dually, the
boundary operators...
- and
coboundary operators admit similar structures in dual
space called the dual
boundary Δ^{\displaystyle {\hat {\Delta }}} and dual
coboundary ∇^{\displaystyle...
