nLab
local coefficient bundle

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cohomology

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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.

Revised on August 29, 2012 02:13:11 by Urs Schreiber (82.113.121.75)