Standard complexes of presentations and the fixed point property

IVÁN SADOFSCHI COSTA

Kortrijk

Conferencia; Nielsen Theory and Related Topics; 2019

Algebraic Topology & Group Theory research group, KU Leuven

In 1969, R. H. Bing asked the following question: Is there a 2-dimensional compact polyhedron with the fixed point property and even Euler characteristic? In this talk, I will explain how to obtain such a space from a group presentation satisfying certain algebraic condition. We will see how this idea can be used to answer another question due to Bing: Is the fixed point property homotopy invariant for 2-dimensional polyhedra? I will also present results obtained in joint work with Jonathan Barmak that give a negative answer to the first question when the fundamental group is abelian or a finite subgroup of SO(3).