Chart description for genus-two Lefschetz fibrations and a theorem on their stabilization

TL;DR

This paper introduces a chart description method for genus-two Lefschetz fibrations and proves that any such fibration can be stabilized through fiber-sum with basic fibrations, advancing the understanding of their structure.

Contribution

It develops a new chart description framework for genus-two Lefschetz fibrations and establishes a stabilization theorem using fiber-sum operations.

Findings

Introduced a chart description for genus-two Lefschetz fibrations

Proved stabilization of any genus-two Lefschetz fibration via fiber-sum

Enhanced understanding of the structure and classification of these fibrations

Abstract

Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for genus-two Lefschetz fibrations, and show that any genus-two Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.