Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.19828

The orientation-reversing minimal stretch factor problem in small genus

Pierre Dehornoy·Erwan Lanneau·Livio Liechti·Quentin Perroud
View original source ↗Read source document ↗Export metadata ↓

Abstract

We determine the minimal stretch factors among all orientation-reversing pseudo-Anosov mapping classes of the closed orientable surfaces of genus two, three and four.

Explore related subjects

math.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Pierre Dehornoy, Erwan Lanneau, Livio Liechti, Quentin Perroud. 2026-10-14. The orientation-reversing minimal stretch factor problem in small genus. https://arxiv.org/abs/2610.19828

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The fundamental quandle of ribbon concordances

We describe the fundamental quandle of a properly embedded surface $Σ$ (possibly with boundary) in $\mathbb{R}^{3}\times I$ and derive its presentation in terms of its motion picture. Our study is based on the topological definition of the fundamental quandle. We prove that a ribbon concordance $C$ from a classical knot $K_1$ to a classical knot $K_0$ gives rise to a quandle monomorphism $Q(K_0)\hookrightarrow Q(C)$ and a quandle epimorphism $Q(K_1)\twoheadrightarrow Q(C)$.

math.GT↗
arXiv2026

An embedding of spherical quandles into Lie groups

We construct smooth embeddings of spherical quandles into conjugation quandles of Lie groups, where the ambient Lie groups can be chosen to be orthogonal, Spin, or Pin groups. Moreover, in dimensions $1$ and $3$, we compare our embeddings with those due to Bergman and Akita.

math.GT↗
arXiv2026

Minima of geodesic length functions for non-uniform filling systems

Kerckhoff proved that the geodesic length function $\ell_Ω$ of a filling $Ω$ on $S_g$ attains a unique minimum in Teichmüller space. Recent work of Ernesto Girondo et al. computed these minima for uniform fillings using the algebraic machinery of dessins d'enfants and Grothendieck-Belyi surfaces. We present an elementary optimization approach for $4$-regular topological uniform fillings, bypassing this framework. Furthermore, we analyze two special classes of non-uniform $4$-regular fillings using fat graphs and optimization techniques. We explicitly compute their minima and prove that in both classes, the minimum of these length functions is attained at a triangle surface.

math.GT↗