A property of $\gamma$ curves derived from topology of relative trisected 4-manifolds

TL;DR

This paper explores the properties of gamma curves in the topology of relative trisected 4-manifolds, showing how they relate via Torelli group actions and connecting to cork twists.

Contribution

It extends the understanding of gamma curves in relative trisected 4-manifolds and links their properties to Torelli group elements and cork twists.

Findings

Any two (g; 0, 0, k)-trisected 4-manifolds are related by Torelli group elements.

Torelli group elements can be replaced by Johnson kernel elements.

The study connects gamma curve properties to cork twists.

Abstract

Any two $(g; 0, 0, k)$-trisected closed 4-manifolds are related to each other by cutting and regluing in regard to $\gamma$ curves by an element of the Torelli group. Moreover, Lambert-Cole showed that this element can be replaced by an element of the Johnson kernel. We consider similar situation in the relative case. Furthermore, we relate this situation to cork twist.