9
votes
1answer
600 views

Are bundle gerbes bundles of algebras?

The category of line bundles (possibly with connection) on a smooth manifoldĀ M can be defined in two different ways: The first definition uses transition functions that satisfy a cocycle condition ...
13
votes
5answers
1k views

What do gerbes and complex powers of line bundles have to do with each other?

We all know how to take integer tensor powers of line bundles. I claim that one should be able to also take fractional or even complex powers of line bundles. These might not be line bundles, but ...