Spin Lefschetz fibrations are abundant

Mihail Arabadji and R. İnanç Baykur

Vol. 326 (2023), No. 1, 1–16

DOI: 10.2140/pjm.2023.326.1

Abstract

We prove that any finitely presented group can be realized as the fundamental group of a spin Lefschetz fibration over the $2$-sphere. We also show that any admissible lattice point in the symplectic geography plane below the Noether line can be realized by a simply connected spin Lefschetz fibration.

Keywords

Lefschetz fibration, symplectic 4-manifold, spin structure, mapping class groups

Mathematical Subject Classification

Primary: 57K20, 57K43, 57R15

Milestones

Received: 31 July 2023

Revised: 15 November 2023

Accepted: 17 November 2023

Published: 14 December 2023