Geometry & Topology, Vol. 5 (2001) Paper no. 4, pages 109--125.

Cobordisms and Reidemeister torsions of homotopy lens spaces

Siddhartha Gadgil

Abstract. We show that any 3-dimensional homotopy lens space M^3 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 \pi _1(M) on the universal cover of M embeds in an orthogonal action on S^7.

Keywords. Reidemeister torsion, lens space, multi-signature, s-cobordism

AMS subject classification. Primary: 57M60, 57N70. Secondary: 57R65, 57R80.

DOI: 10.2140/gt.2001.5.109

E-print: arXiv:math.GT/0005043

Submitted to GT on 20 November 2000. Paper accepted 30 January 2001. Paper published 24 February 2001.

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Siddhartha Gadgil
Department of Mathematics
SUNY at Stony Brook
Stony Brook, NY 11794, USA

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