The string coproduct "knows" Reidemeister/Whitehead torsion

Abstract

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.

References in corpus (2)

• The homotopy invariance of the string topology loop product and string bracket
• A cellular topological field theory

Cited by in corpus (1)

• On the string topology of symmetric spaces of higher rank