The fixed point property for 2-dimensional polyhedra

JONATHAN ARIEL BARMAK; IVÁN SADOFSCHI COSTA

Waco

Conferencia; 50th Spring Topology and Dynamical Systems Conference; 2016

In 1969 R.H. Bing asked the following question. Is there a 2-dimensional polyhedron K with even Euler characteristic such that each self map of K has a fixed point? This question is related to the (non) homotopy invariance of the fixed point property. We will show how Nielsen fixed point theory along with a homotopy classification theorem by W. Browning, imply that no such space exists if we require the fundamental group to be abelian. An example recently found by I. Sadofschi Costa, however, shows that the answer to Bing's question is affirmative.