Edge Preserving Maps of the Curve Graphs in Low Genus

2018/03/21 by Elmas Irmak, Irmak, Elmas
Mathematics · #20F38 #57N05 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20F38 #msc:57N05

paper · pdf · doi:10.48550/arxiv.1803.08806

25 pages, 14 figures. arXiv admin note: text overlap with arXiv:1708.05290

arxiv created 2018/03/21 · arxiv updated 2018/03/26

Abstract

Let R be a compact, connected, orientable surface of genus g with n boundary components. Let C(R) be the curve graph of R. We prove that if g=0, n ≥ 5 or g=1, n ≥ 3, and λ: C(R) \rightarrowC(R) is an edge preserving map, then λ is induced by a homeomorphism of R, and this homeomorphism is unique up to isotopy.

Citations

• Edge Preserving Maps of the Nonseparating Curve Graphs, Curve Graphs and\n Rectangle Preserving Maps of the Hatcher-Thurston Graphs

Related

• Edge Preserving Maps of the Nonseparating Curve Graphs, Curve Graphs and\n Rectangle Preserving Maps of the Hatcher-Thurston Graphs
• Edge-preserving maps of curve graphs
• Graph morphisms and exhaustion of curve graphs of low-genus surfaces
• Automorphisms of the fine 1-curve graph
• Hyperbolic isometries of the fine curve graph of higher genus surfaces