Dehn-Fried surgeries on non-transitive expansive flows

Abstract

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

24 pages, 5 figures