2014/08/03 by Camille Horbez, Horbez, Camille · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.1408.0543
v3: Final version, to appear in the Israel Journal of Mathematics. Section 3, regarding the definition and properties of geometric trees, has been rewritten to improve the exposition, following a referee's suggestion
arxiv created 2016/04/24 · arxiv updated 2016/04/26
Let G be a countable group that splits as a free product of groups of the form G=G1∗…∗ Gk∗ FN, where FN is a finitely generated free group. We identify the closure of the outer space PO(G,\G1,…,Gk\) for the axes topology with the space of projective minimal, very small (G,\G1,…,Gk\)-trees, i.e. trees whose arc stabilizers are either trivial, or cyclic, closed under taking roots, and not conjugate into any of the Gi'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,\G1,…,Gk\)-tree has at most 2N+2k-2 orbits of branch points.