On a conjecture of Daniel H. Gottlieb

Details On a conjecture of Daniel H. Gottlieb On a conjecture of Daniel H. Gottlieb

2007-02-27

arxiv.org/abs/math/0702826v2

Algebraic & Geometric Topology 7 (2007) 779-784

Mathematics

Algebraic Topology

5 pages, version 2 with minor modifications, to appear in Algebraic and Geometric Topology

Scientific paper

10.2140/agt.2007.7.779

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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