Reidemeister torsion for flat superconnections

Abstract

We use higher parallel transport -more precisely, the integration A ∞ -functor constructed in [3, 1] -to define Reidemeister torsion for flat superconnections. We conjecture a version of the Cheeger-Müller theorem, namely that the combinatorial Reidemeister torsion coincides with the analytic torsion defined by Mathai and Wu [12].

On a twisted Reidemeister torsion

“…Remark. In [1], C. Arias Abad and F. Schätz defined a Reidemeister torsion for flat superconnections. Their construction can be applied to (m • (K, E), ∂ t ) and, as F. Schätz explained to me, their torsion coincides (up to elements of unit norm) with the one defined above.…”

The A∞ de Rham Theorem and Integration of Representations up to Homotopy

“…Moreover, we establish that the integration process lands in the category of unital representations up to homotopy. Observe that the unitality condition is important for the construction of Reidemeister torsion of flat superconnections given in [5] and also comes up naturally in the construction of the differentiation functor Ψ :…”