Lefschetz fibrations and Torelli groups

TL;DR

This paper constructs explicit examples of Lefschetz fibrations and surface bundles with monodromies in the Torelli group, revealing new structures and infinite families beyond holomorphic cases.

Contribution

It provides explicit constructions of fiber sum indecomposable Lefschetz fibrations and surface bundles with Torelli group monodromies, including infinitely many non-holomorphic examples.

Findings

Explicit examples of Lefschetz fibrations with Torelli monodromies

Construction of fiber sum indecomposable surface bundles in Torelli group

Infinite non-holomorphic Lefschetz fibrations

Abstract

For each g > 2 and h > 1, we explicitly construct (1) fiber sum indecomposable relatively minimal genus g Lefschetz fibrations over genus h surfaces whose monodromies lie in the Torelli group, (2) fiber sum indecomposable genus g surface bundles over genus h surfaces whose monodromies are in the Torelli group (provided g > 3), and (3) infinitely many genus g Lefschetz fibrations over genus h surfaces that are not fiber sums of holomorphic ones.