Genus one Lefschetz fibrations on disk cotangent bundles of surfaces

TL;DR

This paper constructs a genus one Lefschetz fibration on the disk cotangent bundle of any closed surface, providing explicit open book decompositions compatible with the canonical contact structure.

Contribution

It introduces a genus one Lefschetz fibration on disk cotangent bundles of surfaces, linking it to explicit open book decompositions for contact geometry.

Findings

Lefschetz fibration of genus one on disk cotangent bundles

Explicit open book decompositions compatible with contact structures

Applicable to all closed orientable surfaces

Abstract

We describe a Lefschetz fibration of genus one on the disk cotangent bundle of any closed orientable surface S. As a corollary, we obtain an explicit genus one open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of S.