Superinjective Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces

Details Superinjective Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces Superinjective Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces

2009-08-20

arxiv.org/abs/0908.2972v3

Mathematics

Geometric Topology

In response to comments from the referee, the paper was shortened and reorganized. A minor mistake pointed out by the referee

Scientific paper

10.3906/mat-0912-66

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 $g +
n \geq 5$, where $g$ is the genus of the surface and $n$ is the number of the
boundary components.

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