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Algebraic Topology and Physics Seminar, Week 1

Title: “Loop Differential K-theory”
Speaker: Scott Wilson, Queens College, CUNY
Date: Tuesday, January 24, 2012
Time: 10:00am – 11:30am
Place: Seminar Room 313, Simons Center





I’ll introduce an extension of the Chern-Simons form, associated to a path of connections on a bundle over a manifold M, to a differential form on the free loop space LM. This form determines an equivalence relation on the set of connections on a bundle, and can be used to define a functor from manifolds to rings, in much the same way that differential K-theory is defined by Simons and Sullivan using the Chern-Simons form. This ring, loop differential K-theory, yields a refinement of differential K-theory, and in particular includes holonomy information in its classes. Additionally, loop differential K-theory is strictly coarser than the Grothendieck group of bundles with connection up to gauge equivalence. This is joint work with Thomas Tradler and Mahmoud Zeinalian.