Superinjective simplicial maps of the two-sided curve complexes on nonorientable surfaces
Volume 249 / 2020
Fundamenta Mathematicae 249 (2020), 211-260
MSC: Primary 57N05; Secondary 20F38.
DOI: 10.4064/fm504-6-2019
Published online: 23 December 2019
Abstract
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 $H=[h]$.
