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Injective simplicial maps of the complex of arcs on nonorientable surfaces

Elmas Irmak
Algebraic & Geometric Topology 9 (2009) 2055–2077
DOI: 10.2140/agt.2009.9.2055
Abstract

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.

Keywords
mapping class group, complex of arcs, nonorientable surface
Mathematical Subject Classification 2000
Primary: 57M99
Secondary: 20F38
References
Publication
Received: 13 August 2008
Accepted: 11 September 2009
Published: 14 October 2009
Authors
Elmas Irmak
Department of Mathematics & Statistics
Bowling Green State University
Bowling Green, OH 43403
USA
http://www-math.bgsu.edu/~eirmak