Homotopy invariants and the fixed point property

JONATHAN ARIEL BARMAK

Binghamton

Congreso; Binghamton University Graduate Conference in Algebra and Topology; 2019

Binghamton University

A space has the fixed point property (FPP) if every self map has a fixed point. We know that disks and, in general, compact polyhedra with trivial rational homology have the FPP. On the other hand, polyhedra with non-trivial rational H1 do not have the FPP. The connection between the FPP and homology/homotopy groups is very weak when we consider more general (non-Hausdorff) spaces. We will see that given any compact CW-complex X there is a (finite!) topological space with the FPP having the same homotopy invariants as X.