New examples of Anosov flows on higher dimensional manifolds which fibre over $3$-dimensional Anosov flows

TL;DR

This paper constructs new non-algebraic Anosov flows in higher dimensions by suspending the fundamental group action of a finite cover of a known flow, expanding the class of such flows.

Contribution

It introduces a novel method to generate higher-dimensional Anosov flows that fiber over 3-dimensional flows, using suspension of fundamental group actions.

Findings

Constructed non-algebraic Anosov flows in dimensions 7 and higher.

Demonstrated these flows fiber over 3-dimensional Anosov flows.

Extended the known examples of Anosov flows to higher dimensions.

Abstract

We construct non-algebraic Anosov flows in dimension $3+2n$, $n\geq 2$, by suspending the action of the fundamental group of a finite cover of the Bonatti-Langevin flow.