Self coincidence numbers and the fundamental group
Abstract
For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M,N;f) of continuous maps homotopic to f:M--> N.We show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f equals zero. Since the self intersection number is equal to the product of the degree of f and the Euler--Poincare number of N, we obtain results related to earlier results about the evaluation map and the Euler--Poincare number.
Cite
@article{arxiv.math/0702236,
title = {Self coincidence numbers and the fundamental group},
author = {Daniel Henry Gottlieb},
journal= {arXiv preprint arXiv:math/0702236},
year = {2007}
}
Comments
10 pages. his paper adds a hypothesis to Proposition 4.2 which renders it true. Thomas Schick found that the conjectures in section 4 were false. I added a revised conjecture, which Thomas Schick and Andreas Thom seem to have shown is true