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https://hdl.handle.net/2440/3741
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Type: | Journal article |
Title: | On the homotopy invariance of L2 torsion for covering spaces |
Author: | Varghese, M. Rothenberg, M. |
Citation: | Proceedings of the American Mathematical Society, 1998; 126(3):887-897 |
Publisher: | AMER MATHEMATICAL SOC |
Issue Date: | 1998 |
ISSN: | 0002-9939 1088-6826 |
Abstract: | <p>We prove the homotopy invariance of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding="application/x-tex">L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> cohomology of the covering space vanishes, the homotopy invariance was established by Lück. We also give some applications of our results.</p> |
DOI: | 10.1090/s0002-9939-98-04595-x |
Published version: | http://dx.doi.org/10.1090/s0002-9939-98-04595-x |
Appears in Collections: | Aurora harvest Pure Mathematics publications |
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