# Higher holonomy and representations up to homotopy

### Jim Stasheff (University of Pennsylvania)

16-Dec-2021, 16:15-17:15 (14 months ago)

Abstract: "Given a connection for a smooth vector bundle $p:E\to M$, 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.

Classical parallel transport with respect to smooth paths in the base space $M$ and the correspondence with representations of $\pi_1(M)$ will be recalled briefly, but no familiarity with differential graded vector bundles with generalized flat connections will be assumed."

mathematical physicsalgebraic geometrydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic