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Superinjective simplicial maps of the two-sided curve complexes on nonorientable surfaces

Volume 249 / 2020

Elmas Irmak, Luis Paris Fundamenta Mathematicae 249 (2020), 211-260 MSC: Primary 57N05; Secondary 20F38. DOI: 10.4064/fm504-6-2019 Published online: 23 December 2019


Let $N$ be a compact, connected, nonorientable surface of genus $g\geq 5$ with $n\geq 0$ boundary components. Let $\mathcal {T}(N)$ be the two-sided curve complex of $N$. If $\lambda :\mathcal {T}(N) \rightarrow \mathcal {T}(N)$ is a superinjective simplicial map, then there exists a homeomorphism $h : N \rightarrow N$ unique up to isotopy such that $H(\alpha ) = \lambda (\alpha )$ for every vertex $\alpha $ in $\mathcal {T}(N)$ where $H=[h]$.


  • Elmas IrmakDepartment of Mathematics
    University of Michigan
    Ann Arbor, MI 48109, U.S.A.
  • Luis ParisIMB, UMR 5584, CNRS
    Université Bourgogne Franche-Comté
    21000 Dijon, France

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