Israel Journal of Mathematics

, Volume 221, Issue 1, pp 179–234 | Cite as

The boundary of the outer space of a free product

  • Camille HorbezEmail author


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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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques d’OrsayUniversité Paris SudOrsayFrance

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