On sections of hyperelliptic Lefschetz fibrations

TL;DR

This paper constructs a specific relation among Dehn twists in the mapping class group, providing a detailed topological description of certain sections in hyperelliptic Lefschetz fibrations of genus g.

Contribution

It introduces a new relation among Dehn twists that explicitly describes the topology of sections in hyperelliptic Lefschetz fibrations.

Findings

Explicit relation among Dehn twists for genus g surfaces

Topological description of 4g+4 disjoint (-1)-sections

Application to hyperelliptic Lefschetz fibrations on complex manifolds

Abstract

We construct a relation among right-handed Dehn twists in the mapping class group of a compact oriented surface of genus g with 4g+4 boundary components. This relation gives an explicit topological description of 4g+4 disjoint (-1)-sections of a hyperelliptic Lefschetz fibration of genus g on the manifold {CP}^2#(4g+5){-CP}^2.