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arXiv · 2601.15651

An index theory for transverse trajectories

Nelson Schuback
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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.

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Nelson Schuback. 2026-01-22. An index theory for transverse trajectories. https://arxiv.org/abs/2601.15651

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