A hyperbolicity criterion for subgroups of RF(G)

作者：Mueller Thomas

来源：Abhandlungen aus Dem Mathematischen Seminar der Universitat Hamburg, 2010, 80(2): 193-205.

DOI：10.1007/s12188-010-0045-9

• Hyperbolic subgroup
• Local incompatibility
• Free product
• Local-global principle

This paper continues the investigation of the groups RF(G) first introduced in the forthcoming book of Chiswell and Muller "A Class of Groups Universal for Free R-Tree Actions" and in the article by Muller and Schlage-Puchta (Abh. Math. Semin. Univ. Hambg. 79:193-227, 2009). We establish a criterion for a family {H(sigma)} of hyperbolic subgroups H(sigma) <= RF(G) to generate a hyperbolic subgroup isomorphic to the free product of the H(sigma) (Theorem 1.2), as well as a local-global principle for local incompatibility (Theorem 4.1). In conjunction with the theory of test functions as developed by Muller and Schlage-Puchta (Abh. Math. Semin. Univ. Hambg. 79: 193-227, 2009), these results allow us to obtain a necessary and sufficient condition for a free product of real groups to embed as a hyperbolic subgroup in RF(G) for a given group G (Corollary 5.4). As a further application, we show that the centralizers associated with a family of pairwise locally incompatible cyclically reduced functions in RF(G) generate a hyperbolic subgroup isomorphic to the free product of these centralizers (Corollary 5.2).

• 出版日期2010-11