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On the homotopy invariance of $L^2$ torsion for covering spaces

Author(s): Varghese Mathai; Melvin Rothenberg
Journal: Proc. Amer. Math. Soc. 126 (1998), 887-897.
MSC (1991): Primary 58G11, 58G18, 58G25
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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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Additional Information:

Varghese Mathai
Affiliation: Department of Mathematics, University of Adelaide, Adelaide 5005, Australia
Email: vmathai@maths.adelaide.edu.au

Melvin Rothenberg
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: mel@math.uchicago.edu

DOI: 10.1090/S0002-9939-98-04595-X
PII: S 0002-9939(98)04595-X
Keywords: $L^2$ torsion, invariants, amenable groups, residually finite groups, Whitehead groups, homotopy invariance
Received by editor(s): May 16, 1996
Additional Notes: The second author was supported in part by NSF Grant DMS 9423300
Communicated by: Jozef Dodziuk
Copyright of article: Copyright 1998, American Mathematical Society

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