Coincidence Reidemeister trace and its generalization

Abstract

We give a homotopy invariant construction of the Reidemeister trace for the coincidence of two maps between closed manifolds of not necessarily the same dimensions. It is realized as a homology class of the homotopy equalizer, which coincides with the Hurewicz image of Koschorke's stabilized bordism invariant. To define it, we use a kind of shriek maps appearing string topology. As an application, we compute the coincidence Reidemeister trace for the self-coincidence of the projections of $S^1$-bundles on $\mathbb{C}{P}^n$. We also mention how to relate our construction to the string topology operation called the loop coproduct.

arXiv comment25 pages, the description using Thom spectra is added, the generalization of the Reidemeister trace for three or more maps is deleted