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Cobordisms and Reidemeister torsions of homotopy lens spaces

Siddhartha Gadgil

Geometry & Topology 5 (2001) 109–125

arXiv: math.GT/0005043

Abstract

We show that any 3–dimensional homotopy lens space M3 that is simple-homotopy equivalent to a lens space L(p,q) is topologically s-cobordant to the lens space. It follows that M has the same multi-signature as L(p,q) and the action of π1(M) on the universal cover of M embeds in a free orthogonal action on S7.

Keywords
Reidemeister torsion, lens space, multi-signature, $s$-cobordism
Mathematical Subject Classification 2000
Primary: 57M60, 57N70
Secondary: 57R65, 57R80
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Publication
Received: 20 November 2000
Accepted: 30 January 2001
Published: 24 February 2001
Proposed: Robion Kirby
Seconded: Walter Neumann, Wolfgang Metzler
Authors
Siddhartha Gadgil
Department of Mathematics
SUNY at Stony Brook
Stony Brook
New York 11794
USA