Stasheff J. Higher holonomy. Representations up to homotopy (abstract)

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Speaker: Jim Stasheff

Title: Higher holonomy. Representations up to homotopy

Abstract:
Given a connection for a smooth vector bundle [math]\displaystyle{ p\colon E\to M }[/math], parallel transport with respect to smooth paths in the base space [math]\displaystyle{ M }[/math] provides a correspondence between smooth vector bundles with flat connection on [math]\displaystyle{ M }[/math] and representations of [math]\displaystyle{ \pi_1(M) }[/math]. Based in part on earlier groundbreaking work of K.T. Chen, recently this correspondence has been enhanced to the level of smooth paths (not homotopy classes) in the base space [math]\displaystyle{ M }[/math] and differential graded vector bundles with generalized flat connections.

Video
Slides: StasheffAMVconf2021slides.pdf

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.