Symplectic Lefschetz fibrations with arbitrary fundamental groups

TL;DR

This paper constructs explicit symplectic Lefschetz fibrations with any given fundamental group and explores the properties of sections and monodromy in these fibrations, advancing understanding of their topological and symplectic structures.

Contribution

It provides a method to explicitly build symplectic Lefschetz fibrations with arbitrary fundamental groups and analyzes the numerical and monodromy properties of their sections.

Findings

Explicit construction of symplectic Lefschetz fibrations with prescribed fundamental groups

Analysis of the numerical properties of sections in these fibrations

Relationship between sections and monodromy group structure

Abstract

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections in symplectic Lefschetz fibrations and their relation to the structure of the monodromy group.