The Hamiltonian surface of $\Aut(F_2)$
Group Theory
2025-07-02 v1
Abstract
The group of automorphisms of the free group on two generators is known to act geometrically, in an essentially unique way, on a 2-dimensional CAT(0) space X. We prove that X contains precisely two Hamiltonian surfaces. By this we mean a surface in X which visits every vertex and every edge precisely once.
Keywords
Cite
@article{arxiv.2507.00213,
title = {The Hamiltonian surface of $\Aut(F_2)$},
author = {Sylvain Barré and Mikaël Pichot},
journal= {arXiv preprint arXiv:2507.00213},
year = {2025}
}