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 selfcoincidence 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 arXiv:
 arXiv:1606.07363
 Bibcode:
 2016arXiv160607363T
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology;
 54H25 (primary);
 55P50;
 55T10 (secondary)
 EPrint:
 25 pages, the description using Thom spectra is added, the generalization of the Reidemeister trace for three or more maps is deleted