# Region crossing change on surfaces

## TL;DR

This paper investigates how region crossing change, a local link diagram operation, behaves on surfaces of higher genus, extending the understanding from the well-studied case of the sphere.

## Contribution

It explores the properties and effects of (modified) region crossing change on surfaces with higher genus, expanding the theoretical framework beyond the sphere.

## Key findings

- Behavior of region crossing change on higher genus surfaces analyzed
- Extension of known results from $S^2$ to complex surfaces
- Insights into the modification of link diagrams on complex surfaces

## Abstract

Region crossing change is a local operation on link diagrams. The behavior of region crossing change on $S^2$ is well understood. In this paper, we study the behavior of (modified) region crossing change on higher genus surfaces.