Cobordisms and Reidemeister torsions of homotopy lens spaces

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 $S^7$.