Injective Simplicial Maps of the Complexes of Curves of Nonorientable Surfaces

Details Injective Simplicial Maps of the Complexes of Curves of Nonorientable Surfaces Injective Simplicial Maps of the Complexes of Curves of Nonorientable Surfaces

2012-03-19

arxiv.org/abs/1203.4271v2

Mathematics

Geometric Topology

15 pages, 6 Figures. The paper was shortened and reorganized

Scientific paper

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$
boundary components, and $\mathcal{C}(N)$ be the complex of curves of $N$.
Suppose that $g + n \leq 3$ or $g + n \geq 5$. If $\lambda : \mathcal{C}(N)
\rightarrow \mathcal{C}(N)$ is an injective simplicial map, then $\lambda$ is
induced by a homeomorphism of $N$.

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