Automorphisms of the pants graph of a nonorientable surface

TL;DR

This paper establishes that, for most nonorientable surfaces, the automorphism group of the pants graph aligns with the surface's mapping class group, extending known results from orientable surfaces.

Contribution

It proves the isomorphism between the automorphism group of the pants graph and the mapping class group for nonorientable surfaces, except in low-complexity cases.

Findings

Automorphism group is isomorphic to the mapping class group in most cases.

Identifies exceptions in low-complexity cases.

Extends the understanding of surface symmetries to nonorientable cases.

Abstract

We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.