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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Varghese Mathai and Melvin Rothenberg
Journal: Proc. Amer. Math. Soc. 126 (1998), 887-897
MSC (1991): Primary 58G11, 58G18, 58G25
MathSciNet review: 1469424
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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: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society