On the homotopy invariance of 𝐿² torsion for covering spaces

Mathai, Varghese; Rothenberg, Melvin

doi:10.1090/S0002-9939-98-04595-X

On the homotopy invariance of $L^2$ torsion for covering spaces
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by Varghese Mathai and Melvin Rothenberg PDF

Proc. Amer. Math. Soc. 126 (1998), 887-897 Request permission

Abstract:

We prove the homotopy invariance of $L^2$ torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the $L^2$ cohomology of the covering space vanishes, the homotopy invariance was established by Lück. We also give some applications of our results.

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