Cobordisms and Reidemeister torsions of homotopy lens spaces

Gadgil, Siddhartha¹

¹ Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794, USA

Geometry & topology, Tome 5 (2001) no. 1, pp. 109-125.

Résumé

We show that any 3–dimensional homotopy lens space $M^3$ that is simple-homotopy equivalent to a lens space $L\left(p,q\right)$ is topologically $s$-cobordant to the lens space. It follows that $M$ has the same multi-signature as $L\left(p,q\right)$ and the action of ${\pi }_1\left(M\right)$ on the universal cover of $M$ embeds in a free orthogonal action on $S^7$.

Détail

DOI : 10.2140/gt.2001.5.109

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

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