C*-Categories, Groupoids and Fell Bundles

David O'sullivan (Sheffield University)

Tuesday 24th February, 2015 16:00-17:00 Maths 326


A Fell bundle is a generalised fibre-bundle of Banach spaces living over a topological groupoid. They are perhaps most succinctly described using the language category theory - we ask "If a group is a groupoid with one object, what is a C*-algebra?", the answer being a C*-category. 

To capture the geometry involved we require a version of C*-category that is "continuous" in the same sense as a topological groupoid. However, all that has been explored so far are C*-categories whose set of objects is purely discrete and carries no geometric structure.

In this talk I hope to redress this omission. I also intend to demonstrate how the language of topological C*-categories does indeed capture the notion of a Fell bundle, and how we can extend the topological invariant K-theory to this new construction.

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