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Gerbes over orbifolds and twisted K-theory

Mathematical Physics & Probability

Speaker: Bernardo Uribe, Max Planck Institut fuer Mathematik Bonn
Location: 593 Kerr
Start time: Wed, May 7 2003, 12:10PM

In this talk I will discuss my recent work (with Ernesto Lupercio) on which, following Segal, we associate to every gerbe with connection (B-field) a line bundle with connective structure over the loop orbifold, via a generalized holonomy map. I will show how this line bundle once localized to the inertia orbifold (twisted sectors) produces local coefficients (flat line bundles) for the orbifold cohomology (these coincide with the "inner local systems" in Ruan's theory.) I will also explain how these line bundles are the coefficients that Freed-Hopkins-Teleman use in their work of Twisted equivariant K-theory. When the orbifold is a manifold we recuperate the 2-dimensional TQFT constructed by Gawedzki.

This is a joint analysis-math-physics-geometry-topology seminar