The A-infinity de-Rham theorem and Reidemeister torsion
I will begin by describing the A-infinity version of de-Rham’s theorem, due to Gugenheim, based on Chen’s work on iterated integrals. I will then explain how this theorem leads to a notion of higher parallel transport considered by Igusa and Block-Smith. Finally, I will explain how this higher parallel transport can be used to define Reidemeister torsion for flat superconnections. This talk is based on joint work with F. Schätz.