Cobordisms and Reidemeister torsions of homotopy lens spaces

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 $π_{1} (M)$ on the universal cover of $M$ embeds in a free orthogonal action on $S^{7}$ .

Keywords

Reidemeister torsion, lens space, multi-signature, $s$-cobordism

Mathematical Subject Classification 2000

Primary: 57M60, 57N70

Secondary: 57R65, 57R80

References

Forward citations

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

Volume 5, issue 1 (2001)

Siddhartha Gadgil