Flows of flowable Reeb homeomorphisms

TL;DR

This paper investigates fixed point free homeomorphisms of a band that preserve Reeb foliation leaves, analyzing their behavior as time-one maps of flows and comparing boundary restrictions.

Contribution

It introduces a framework for understanding Reeb homeomorphisms as flow time-one maps and compares boundary flow restrictions.

Findings

Reeb homeomorphisms can be characterized as time-one maps of certain flows.

Boundary flow restrictions provide insights into the structure of these homeomorphisms.

The approach links foliation-preserving homeomorphisms with flow dynamics.

Abstract

We consider a fixed point free homeomorphsim $h$ of the closed band $B=\R\times[0,1]$ which leaves each leaf of a Reeb foliation on $B$ invariant. Assuming $h$ is the time one of various topological flows, we compare the restriction of the flows on the boundary.