#### Volume 14, issue 2 (2014)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
On simplicial maps of the complexes of curves of nonorientable surfaces

### Elmas Irmak

Algebraic & Geometric Topology 14 (2014) 1153–1180
##### Abstract

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components and $\mathsc{C}\left(N\right)$ be the complex of curves of $N$. Suppose that $g+n\le 3$ or $g+n\ge 5$. If $\lambda :\phantom{\rule{0.3em}{0ex}}\mathsc{C}\left(N\right)\to \mathsc{C}\left(N\right)$ is an injective simplicial map, then $\lambda$ is induced by a homeomorphism of $N$. If $\left(g,n\right)\ne \left(1,2\right)$ and $\lambda :\phantom{\rule{0.3em}{0ex}}\mathsc{C}\left(N\right)\to \mathsc{C}\left(N\right)$ is a simplicial map that satisfies the connectivity property, then $\lambda$ is induced by a homeomorphism of $N$.

##### Keywords
mapping class groups, simplicial maps, nonorientable surfaces
Primary: 57M99
Secondary: 20F38