An extended Cheeger–Müller theorem for covering spaces

We generalize a theorem of Bismut–Zhang, which extends the Cheeger–Müller theorem on Ray–Singer torsion and Reidemeister torsion, to the case of infinite Galois covering spaces. Our result is stated in the framework of extended cohomology, and generalizes in this case a recent result of Braverman–Carey–Farber–Mathai. It does not use the determinant class condition and thus also (potentially) generalizes several results on L 2 -torsions due to Burghelea, Friedlander, Kappeler and McDonald. We combine the framework developed by Braverman–Carey–Farber–Mathai on the determinant of extended cohomology with the heat kernel method developed in the original paper of Bismut–Zhang to prove our result.