Dehn-Fried surgeries on non-transitive expansive flows

TL;DR

This paper characterizes when flows obtained by Dehn-Fried surgeries on expansive flows in 3D remain expansive, linking this property to the absence of 1-prong singularities in their foliations.

Contribution

It provides a necessary and sufficient condition for the expansiveness of flows after Dehn-Fried surgery on expansive flows in three dimensions.

Findings

Expansiveness is preserved if and only if stable and unstable foliations lack 1-prong singularities.

The result applies to flows derived from topological pseudo-Anosov flows.

Characterizes the impact of Dehn-Fried surgeries on flow expansiveness.

Abstract

In this paper, we prove that for any flow $\Psi$ obtained by a Dehn-Fried surgery on an expansive (or equivalently topological pseudo-Anosov) flow $\Phi$ in dimension 3, $\Psi$ is expansive if and only if its stable and unstable foliations do not contain $1$-prong singularities.