The string coproduct “knows” Reidemeister/Whitehead torsion

Naef, Florian¹

¹ Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark, School of Mathematics, Trinity College Dublin, Dublin, Ireland

Geometry & topology, Tome 28 (2024) no. 8, pp. 3643-3659.

Résumé

We show that the string coproduct is not homotopy invariant. More precisely, we show that the (reduced) coproducts are different on $L(1,7)$ and $L(2,7)$. Moreover, the coproduct on $L(k,7)$ can be expressed in terms of the Reidemeister torsion and hence transforms with respect to the Whitehead torsion of a homotopy equivalence. The string coproduct can thereby be used to compute the image of the Whitehead torsion under the Dennis trace map.

Détail

DOI : 10.2140/gt.2024.28.3643

Keywords: string topology, lens spaces, Reidemeister torsion, Whitehead torsion

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