Higher Structure Conferences Schätz (changes)

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Z-graded connections and the loop space

Abstract: The pullback of a flat vector bundle from a manifold to its free loop space comes equipped with a canonical automorphism, which is given by the holonomies. I will explain how this generalizes to flat Z-graded connections. By restriction to the based loop space, one obtains an action of the Pontryagin-algebra of chains on a complex. Moreover, an equivariant version of the story seems to provide an interpretation of the Getzler-Jones-Petrack construction of the Bismut-Chern character in terms of derived geometry. The talk relies on ongoing work with Camilo Arias Abad.