English

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}
}