On the homotopy invariance of $L^2$ torsion for covering spaces
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- by Varghese Mathai and Melvin Rothenberg PDF
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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.References
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Additional Information
- Varghese Mathai
- Affiliation: Department of Mathematics, University of Adelaide, Adelaide 5005, Australia
- MR Author ID: 231404
- Email: vmathai@maths.adelaide.edu.au
- Melvin Rothenberg
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- Email: mel@math.uchicago.edu
- 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 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 887-897
- MSC (1991): Primary 58G11, 58G18, 58G25
- DOI: https://doi.org/10.1090/S0002-9939-98-04595-X
- MathSciNet review: 1469424