Abstract: The celebrated Lefschetz-Hopf fixed point theorem asserts that if a selfmap on a finite polyhedron has nonzero Lefschetz trace then every map homotopic to the given map must have a fixed point. While the converse does not hold in general, the vanishing of a more subtle invariant, namely, the Nielsen number, is often sufficient to guarantee that the given map is deformable to be fixed point free. In this talk, I will survey the computation of the Nielsen number of selfmaps on coset spaces of Lie groups.
This talk will be accessible to general faculty.