Injective simplicial maps of the arc complex

By Elmas Irmak, John D. McCarthy. Turkish Journal of Mathematics, 2006

51 citations recorded by the source corpus.

In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of automorphisms of the arc complex is naturally isomorphic to the extended mapping class group of the surface, provided the surface is not a disc, an annulus, a pair of pants, or a torus with one hole. We also show, for each of these special exceptions, that the group of automorphisms of the arc complex is naturally isomorphic to the quotient of the extended mapping class group of the surface by its center.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f34b8fe4ee79959fcacc88e63f1ad07760e1bec7

How researchers see this paper

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In Geometry and Topology

1. Athanase Papadopoulos
2. Mustafa Korkmaz
3. Burak Ozbagci
4. A. Stipsicz
5. Nikolai V. Ivanov

In Mathematical Physics

1. Athanase Papadopoulos
2. Mustafa Korkmaz
3. A. Stipsicz
4. Burak Ozbagci
5. Nikolai V. Ivanov

Citations in the corpus

• On the arc and curve complex of a surface (2009, result): “We note that the proof of Irmak and McCarthy’s result on the automorphisms of the arc complex does not use the result by Ivanov, Korkmaz and Luo.”