Minimal number of self-intersections of the boundary of an immersed surface in the plane

TL;DR

This paper determines the lowest possible number of self-intersections for the boundary of a genus g surface immersed in the plane, providing insights into the geometric complexity of such immersions.

Contribution

It establishes the minimal number of boundary self-intersections for generically immersed surfaces of any genus in the plane, a novel geometric result.

Findings

Calculated minimal self-intersections for various genera

Provided a general formula or bound for minimal intersections

Enhanced understanding of surface immersion complexity

Abstract

We find the minimal number of self-intersections of the boundary of a surface of genus g generically immersed in the plane.