Superinjective Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces

Abstract

We prove that each superinjective simplicial map of the complex of curves of a compact, connected, nonorientable surface is induced by a homeomorphism of the surface, if $(g,n)\in \{(1,0),(1,1),(2,0),(2,1),(3,0)\}$ or $g+n\ge 5$, where $g$ is the genus of the surface and $n$ is the number of the boundary components.

arXiv commentIn response to comments from the referee, the paper was shortened and reorganized. A minor mistake pointed out by the referee was also corrected

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