Infinitely many closed paths in the graph of Anosov flows

TL;DR

This paper investigates the effects of Fried surgeries on Anosov flows in 3-manifolds, demonstrating that certain suspension flows admit infinitely many pairs of periodic orbits with self-equivalent flows after surgery.

Contribution

It establishes the existence of infinitely many pairs of periodic orbits in some suspension Anosov flows that yield flows equivalent to the original after non-trivial Fried surgeries.

Findings

Existence of infinitely many such pairs in some suspension flows

Fried surgeries can produce flows equivalent to the original

Insights into the structure of Anosov flows and their surgeries

Abstract

Given an Anosov flow on a closed 3-manifold, we are interested in the problem of whether or not making non-trivial Fried surgeries along a finite set of periodic orbits can produce a flow equivalent to itself. We show that for some suspension Anosov flows, there exist infinitely many pairs of periodic orbits satisfying this property.