#### Volume 5, issue 1 (2001)

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Cobordisms and Reidemeister torsions of homotopy lens spaces

Geometry & Topology 5 (2001) 109–125
 arXiv: math.GT/0005043
##### Abstract

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 ${S}^{7}$.

##### Keywords
Reidemeister torsion, lens space, multi-signature, $s$-cobordism
##### Mathematical Subject Classification 2000
Primary: 57M60, 57N70
Secondary: 57R65, 57R80