2016/06/23 by Mitsunobu Tsutaya, Tsutaya, Mitsunobu
Mathematics · Physics and Astronomy · #54H25 (primary) #55P50 #55T10 (secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:54H25 #msc:55P50 #msc:55T10
paper · pdf · doi:10.48550/arxiv.1606.07363
25 pages, the description using Thom spectra is added, the generalization of the Reidemeister trace for three or more maps is deleted
openalex publication_date 2016/06/23 · arxiv created 2016/08/10 · arxiv updated 2016/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S1-bundles on ℂPn. We also mention how to relate our construction to the string topology operation called the loop coproduct.