The fixed point property everywhere

JONATHAN ARIEL BARMAK

Seúl

Congreso; International Congress of Mathematicians; 2014

If K is a polyhedron homotopy equivalent to the 1-dimensional sphere, then there exists a fixed point free map f : K → K. However, we will show that there exists a (non-Hausdorff) space X weak homotopy equivalent to S1 with the fixed point property. Moreover, the latter claim is true if we replace S1 by any connected compact CW-complex.