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On a conjecture of Daniel H. Gottlieb

Thomas Schick·Andreas Thom
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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.

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Thomas Schick, Andreas Thom. 2007-05-01. On a conjecture of Daniel H. Gottlieb. https://doi.org/10.2140/agt.2007.7.779

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