Determinants of Laplacians on discretizations of flat surfaces and analytic torsion (Q2209007)

From the author's abstract: The asymptotic expansion of the determinants of the graph Laplacians associated to discretizations of a half-translation surface endowed with a unitary flat vector bundle is investigated. The author relates the asymptotic expansion of the number of spanning trees and the partition function of cycle-rooted spanning forests, weighted by the monodromy of the unitary connection of the vector bundle, to the corresponding zeta-regularized determinants.