Reidemeister trace and its generalization

2016/09/15 Thu 16:00 - 17:00
Room 604, Building No.6
Mitsunobu Tsutaya
Kyushu University

Reidemeister trace was originally studied in the fixed point problem, which was generalized for the coincidence problem of maps between manifolds of the same dimensions. In this talk, we give a construction of the Reidemeister trace for maps between manifolds of arbitrary dimensions, which is realized as a homology class of the homotopy equalizer. In the construction, shriek maps appearing in string topology play an important role. We also give a technique to compute the Reidemeister trace using Serre spectral sequences.