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arXiv · 2401.01847

Horizontal Goodman surgery and almost equivalence of pseudo-Anosov flows

Chi Cheuk Tsang
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Abstract

We provide an exposition of a `horizontal' generalization of Goodman's surgery operation on (pseudo-)Anosov flows. This operation is performed by cutting along a specific kind of annulus that is transverse to the flow and regluing with a Dehn twist of the appropriate sign. We then show that performing horizontal Goodman surgery on a transitive pseudo-Anosov flow yields an almost equivalent flow, i.e. the original flow and the surgered flow are orbit equivalent after drilling out a finite collection of closed orbits. We obtain some almost equivalence results by applying this theorem on examples of the surgery operation. Along the way, we also show a structural stability result for pseudo-Anosov flows.

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Chi Cheuk Tsang. 2024-01-03. Horizontal Goodman surgery and almost equivalence of pseudo-Anosov flows. https://arxiv.org/abs/2401.01847

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