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arXiv · 2512.07510

A foliated viewpoint on homotopy Brouwer theory

Nelson Schuback
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Abstract

Brouwer homeomorphisms are fixed-point-free, orientation-preserving homeomorphisms of the plane. In recent years, their dynamics have been mostly studied through two complementary approaches, one introduced by Handel and the other by Le Calvez, each offering a distinct perspective on the behavior of Brouwer homeomorphisms. In this work, we present a unified framework that allows Le Calvez's foliated methods to recover, and in some cases improve, the classical results of Handel's theory.

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Nelson Schuback. 2025-12-08. A foliated viewpoint on homotopy Brouwer theory. https://arxiv.org/abs/2512.07510

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