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

Speaker: Jim Stasheff

Title: Higher holonomy. Representations up to homotopy

Abstract:
Given a connection for a smooth vector bundle $p\colon E\to M$, parallel transport with respect to smooth paths in the base space $M$ provides a correspondence between smooth vector bundles with flat connection on $M$ and representations of $\pi _{1}(M)$. 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 $M$ 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.