On the homotopy invariance of 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 | References | Similar Articles | Additional Information

Abstract: We prove the homotopy invariance of 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 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:
https://doi.org/10.1090/S0002-9939-98-04595-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