Isomorphisms between curve graphs of infinite-type surfaces are geometric

2017/06/12 by Jesús Hernández Hernández, Hernández, Jesús Hernández, Israel Morales +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.1706.03697

12 pages, 5 figures

arxiv created 2017/06/12 · openalex publication_date 2017/06/12 · arxiv updated 2017/06/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let ϕ:C(S)\toC(S') be a simplicial isomorphism between the curve graphs of two infinite-type surfaces. In this paper we show that in this situation S and S' are homeomorphic and ϕ is induced by a homeomorphism h:S→ S'.

Cited by

• Non-amenability of mapping class groups of infinite-type surfaces and graphs

Related

• Curve graphs on surfaces of infinite type
• Automorphism groups of simplicial complexes of infinite type surfaces
• Edge-preserving maps of curve graphs
• Automorphisms of the fine curve graph
• Automorphisms of the fine curve graph