On simplicial maps of the complexes of curves of nonorientable surfaces

Irmak, Elmas

doi:10.2140/agt.2014.14.1153

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On simplicial maps of the complexes of curves of nonorientable surfaces

Elmas Irmak

Algebraic & Geometric Topology 14 (2014) 1153–1180

DOI: 10.2140/agt.2014.14.1153

Abstract

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components and $C (N)$ be the complex of curves of $N$ . Suppose that $g + n \leq 3$ or $g + n \geq 5$ . If $λ : C (N) \to C (N)$ is an injective simplicial map, then $λ$ is induced by a homeomorphism of $N$ . If $(g, n) \neq (1, 2)$ and $λ : C (N) \to C (N)$ is a simplicial map that satisfies the connectivity property, then $λ$ is induced by a homeomorphism of $N$ .

Keywords

mapping class groups, simplicial maps, nonorientable surfaces

Mathematical Subject Classification 2010

Primary: 57M99

Secondary: 20F38

References

Publication

Received: 10 February 2013

Revised: 18 September 2013

Accepted: 19 September 2013

Published: 21 March 2014

Authors

Elmas Irmak
Department of Mathematics and Statistics Bowling Green State University Bowling Green, OH 43403 USA
http://www-math.bgsu.edu/~eirmak

Volume 14, issue 2 (2014)