An index theory for transverse trajectories
Dynamical Systems
2026-01-23 v1 General Topology
Abstract
In this work, we present an alternative definition of the Le Roux index, which generalizes the Poincar\'e-Hopf index for non-singular planar flows to the broader setting of Brouwer homeomorphisms. This new approach answers a question raised by Le Roux by establishing a connection between the index of a Brouwer homeomorphism and the structure of its transverse foliations, in the sense of Le Calvez.
Cite
@article{arxiv.2601.15651,
title = {An index theory for transverse trajectories},
author = {Nelson Schuback},
journal= {arXiv preprint arXiv:2601.15651},
year = {2026}
}
Comments
22 pages, 9 figures