Arbitrarily large veering triangulations with a vanishing taut polynomial

TL;DR

This paper constructs a sequence of complex veering triangulations with infinitely increasing tetrahedra count, demonstrating that their taut polynomials can vanish, revealing new insights into the structure of non-fibered Anosov flows.

Contribution

It introduces a sequence of large veering triangulations with vanishing taut polynomials, expanding understanding of their relation to non-fibered Anosov flows.

Findings

Constructed sequences with unbounded tetrahedra count

Demonstrated vanishing taut polynomials in these sequences

Linked veering triangulations to non-circular Anosov flows

Abstract

Landry, Minsky, and Taylor introduced an invariant of veering triangulations called the taut polynomial. Via a connection between veering triangulations and pseudo-Anosov flows, it generalizes the Teichm\"uller polynomial of a fibered face of the Thurston norm ball to (some) non-fibered faces. We construct a sequence of veering triangulations, with the number of tetrahedra tending to infinity, whose taut polynomials vanish. These veering triangulations encode non-circular Anosov flows transverse to tori.