Injective simplicial maps of the complex of arcs on nonorientable surfaces

Irmak, Elmas

doi:10.2140/agt.2009.9.2055

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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

Volume 9, issue 4 (2009)