Embedding groups of graph automorphisms in surfaces |
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Authors: | Jérôme E Los |
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Institution: | a LATP, CNRS, UMR 6632, Universite de Provence, 39 rue F. Joliot Curie, 13453 Marseille Cedex, 13, France b Department of Mathematics, Tufts University, Medford, MA 02155, USA |
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Abstract: | Necessary and sufficient conditions (n.a.s.c) are found for a subgroup of the automorphism group of a finite graph to be realizable as the restriction to an invariant spine of some group of homeomorphisms of a compact surface. Also, n.a.s.c. are found for the restricted case when the surface is required to be orientable. The conditions are formulated in terms of the action of stabilizers of vertices on their stars. In both cases, a parametrization of the possible representations is given. Several examples are treated, as well as an application to deciding whether a given finite group of outer automorphisms of a free group is realizable via a surface homeomorphism. |
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Keywords: | Primary: 37E25 14J50 Secondary: 37E30 57S17 20F34 |
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