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 to an aspherical CW–complex with non-zero Euler characteristic can have non-trivial degree (suitably defined) only if the centralizer of the image of the fundamental group of 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 to are contractible.
We use –Betti numbers and homological algebra over von Neumann algebras to prove the modified conjecture.
Citation
Thomas Schick. Andreas Thom. "On a conjecture of Gottlieb." Algebr. Geom. Topol. 7 (2) 779 - 784, 2007. https://doi.org/10.2140/agt.2007.7.779
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