nLab local coefficient bundle

Contents

Context

Bundles

bundles

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

In the context of twisted cohomology a cocycle on a space XX with coefficients in a coefficient object VV is not quite a direct morphism XVX \to V as in ordinary GG-cohomology, but is instead a section of a VV-fiber ∞-bundle EXE \to X over XX. This is called the local coefficient bundle for the given twisted cohomology. Its class [E]H 1(X,Aut(V))[E] \in H^1(X, \mathbf{Aut}(V)) is the twist.

References

Local coefficient bundles in the context of twisted ordinary cohomology:

Last revised on September 10, 2020 at 06:11:53. See the history of this page for a list of all contributions to it.