Injective simplicial maps of the complex of arcs on nonorientable surfaces

Irmak, Elmas¹

¹Department of Mathematics & Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

Algebraic and Geometric Topology, Tome 9 (2009) no. 4, pp. 2055-2077

Résumé

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.

Détail

DOI : 10.2140/agt.2009.9.2055

Keywords: mapping class group, complex of arcs, nonorientable surface

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