A Foliated Viewpoint on homotopy Brouwer Theory

Brouwer homeomorphisms are orientation-preserving, fixed-point-free homeomorphisms of the plane. In recent years, their dynamics have mainly been studied through two complementary approaches: one introduced by Handel and the other by Le Calvez, each providing a distinct perspective on their behavior. In this talk, we present a unified framework in which the foliated methods developed by Le Calvez recover, and in some cases extend, classical results from Handel’s theory.