Injective Simplicial Maps of the Arc Complex on Nonorientable Surfaces

Details Injective Simplicial Maps of the Arc Complex on Nonorientable Surfaces Injective Simplicial Maps of the Arc Complex on Nonorientable Surfaces

2008-03-04

arxiv.org/abs/0803.0498v1

Mathematics

Geometric Topology

18 pages, 14 figures

Scientific paper

We prove that each injective simplicial map from the arc complex of a
compact, connected, nonorientable surface with nonempty boundary to itself is
induced by a homeomorphism of the surface. We also prove that the automorphism
group of the arc complex is isomorphic to the quotient of the mapping class
group of the surface by its center.

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