Higher holonomy and representations up to homotopy
Jim Stasheff (University of Pennsylvania)
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
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