# nLab local coefficient bundle

### Context

#### Bundles

bundles

fiber bundles in physics

## Context

• dependent type theory

• ## Classes of bundles

• covering space

• numerable bundle

• ## Presentations

• bundle gerbe

• groupal model for universal principal ∞-bundles

• microbundle

• ## Examples

• trivial vector bundle

• tautological line bundle

• basic line bundle on the 2-sphere?
• Hopf fibration

• canonical line bundle

• ## Constructions

• clutching construction

• inner product on vector bundles

• dual vector bundle

• projective bundle

• #### Cohomology

cohomology

# Contents

## Idea

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

Last revised on August 29, 2012 at 02:13:11. See the history of this page for a list of all contributions to it.