I will outline Guggenheim's construction of an A_infty quasi-isomorphism between the dg algebra of differential forms and of singular cochains, respectively, and explain how this allows to systematically assign higher dimensional holonomies to Z-graded connections, thereby recovering and extending results of K. Igusa and Block/Smith. If time permits, I will sketch a definition of combinatorial torsion for flat superconnections which relies on the construction of higher dimensional holonomies. This talk is based on joint work (partly in progress) with Camilo Arias Abad.