2017/08/15 by Elmas Irmak, Irmak, Elmas · 1 citation
Computer Science · Mathematics · #20F38 #57N05 #Combinatorics #Computational Geometry and Mesh Generation #Discrete mathematics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Graph #Group Theory (math.GR) #Homeomorphism (graph theory) #Isotopy #Lambda #Mathematics #Physics #Rectangle #Surface (topology) #math.GR #math.GT #msc:20F38 #msc:57N05
paper · pdf · doi:10.48550/arxiv.1708.05290
38 pages, 25 figures. Changed the statement of Theorem 1.3 and gave more explanation in some proofs
openalex publication_date 2017/08/15 · arxiv created 2019/06/12 · arxiv updated 2019/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Let R be a compact, connected, orientable surface of genus g with n\nboundary components with g \≥ 2, n \≥ 0. Let \N(R) be the\nnonseparating curve graph, \C(R) be the curve graph and\n\HT(R) be the Hatcher-Thurston graph of R. We prove that if\n\λ : \N(R) \→\N(R) is an edge-preserving map,\nthen \λ is induced by a homeomorphism of R. We prove that if \θ :\n\C(R) \→ \C(R) is an edge-preserving map, then\n\θ is induced by a homeomorphism of R. We prove that if R is closed\nand \τ: \HT(R) \→\HT(R) is a rectangle\npreserving map, then \τ is induced by a homeomorphism of R. We also prove\nthat these homeomorphisms are unique up to isotopy when (g, n) \≠ (2, 0).\n