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Abstract
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We prove that each injective simplicial map from the complex of arcs 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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Keywords
mapping class group, complex of arcs, nonorientable surface
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Mathematical Subject Classification 2000
Primary: 57M99
Secondary: 20F38
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Publication
Received: 13 August 2008
Accepted: 11 September 2009
Published: 14 October 2009
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