Positive Dehn Twist Expression for a $\mathbb{Z}_3$ action on $\Sigma_g$

TL;DR

This paper constructs a positive Dehn twist expression for a specific cyclic group action on a surface, and computes the invariants of the associated symplectic 4-manifolds, advancing understanding of surface symmetries and 4-manifold topology.

Contribution

It provides an explicit positive Dehn twist factorization for a $bZ_3$ action on surfaces with fixed points, linking surface symmetries to symplectic 4-manifold invariants.

Findings

Explicit Dehn twist expression for $bZ_3$ action on $Sigma_g$

Computed homeomorphism invariants of resulting symplectic 4-manifolds

Enhanced understanding of surface symmetries and 4-manifold invariants

Abstract

A positive Dehn twist product for a $\mathbb{Z}_3$ action with $g+2$ fixed points on the 2-dimensional closed, compact, oriented surface $\Sigma_g$ is presented. The homeomorphism invariants of the resulting symplectic 4-manifolds are computed.