On a conjecture of Daniel H. Gottlieb
Algebraic Topology
2014-10-01 v2
Abstract
We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of X is trivial. As a corollary we show that in the above situation all components of non-zero degree maps in the space of maps from X to Y are contractible.
Cite
@article{arxiv.math/0702826,
title = {On a conjecture of Daniel H. Gottlieb},
author = {Thomas Schick and Andreas Thom},
journal= {arXiv preprint arXiv:math/0702826},
year = {2014}
}
Comments
5 pages, version 2 with minor modifications, to appear in Algebraic and Geometric Topology