On the Complex of Separating meridians in Handlebodies

TL;DR

This paper proves that for handlebodies of genus at least 6, automorphisms of the complex of separating meridians extend to all meridians, showing they are geometric in nature.

Contribution

It establishes the extendability of automorphisms from separating meridians to all meridians for high-genus handlebodies, confirming their geometric origin.

Findings

Automorphisms of the complex of separating meridians extend to all meridians.

Automorphisms are shown to be geometric.

Valid for handlebodies of genus at least 6.

Abstract

For a handlebody of genus $g\geq6$ it is shown that every automorphism of the complex of separating meridians can be extended to an automorphism on the complex of all meridians and, in consequence, it is geometric.