The boundary of the outer space of a free product |
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Authors: | Camille Horbez |
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Institution: | 1.Laboratoire de Mathématiques d’Orsay,Université Paris Sud,Orsay,France |
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Abstract: | Let G be a countable group that splits as a free product of groups of the form G = G 1 *···* G k * F N , where F N is a finitely generated free group. We identify the closure of the outer space PO(G, {G 1,..., G k }) for the axes topology with the space of projective minimal, very small (G, {G 1,..., G k })-trees, i.e. trees whose arc stabilizers are either trivial, or cyclic, closed under taking roots, and not conjugate into any of the G i ’s, and whose tripod stabilizers are trivial. Its topological dimension is equal to 3N + 2k ? 4, and the boundary has dimension 3N + 2k ? 5. We also prove that any very small (G, {G 1,..., G k })-tree has at most 2N + 2k?2 orbits of branch points. |
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