A combination theorem for strong relative hyperbolicity

By Mahan Mj, Lawrence Reeves. 2006

61 citations recorded by the source corpus.

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Combination Theorem.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fb1c7ff1e1f31b4d041c22c459837e367062dfb5

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quasiconvexity and relatively hyperbolic groups that split (2012, methodology): “relative Dehn functions [19]. Most recently, Mj and Reeves gave a generalization of the Bestvina-Feighn combination theorem that follows Farb’s approach but uses a generalized “partial electrocution” [17]. Their result appears to be a far-reaching generalization at the expense of complex geometric l”
Cannon-Thurston Maps for Surface Groups (2006, background): “ces with Punctures In this section, we shall describe the modiﬁcations necessary to prove Theorem 7.1 for surfaces with punctures. 8.1. Partial Electrocution. Twogeneralreferencesforthis subsectionare[MR08], [MP11], where much of what follows is done in a considerably more general setting. Let M be ”
On hyperbolicity of free splitting and free factor complexes (2012, background): “uces a hyperbolic space. Various versions of this statement have multiple appearances in the literature; see, for example, Lemma 4.5 and Proposition 4.6 in [11], Proposition 7.12 in [7], Lemma 2.3 in [26], Theorem 3.4 in [10], etc. Maher and Schleimer [23] appear to be the ﬁrst once to explicitly no”
Projections and relative hyperbolicity (2010, methodology): “ve result can be seen as a combination theorem formulated in the general setting of metric spaces. To our knowledge, the only other existing metric combination theorem is due to M. Mj and L. Reeves ( [MR]), who adapt the strategy of Bestvina-Feighn (see [BF]). Theorem 0.2 is logically independent of”
A Combination Theorem for Metric Bundles (2009, methodology): “rbolicity of small-girth ladders (Proposition 3.4). In Section 3.2 we break up a big ladder into small-girth ladders and use a consequence (Proposition 1.51) of a combination theorem due to Mj-Reeves [MR08] to conclude that the whole ladder is hyperbolic. 4) In Section 4, we assemble the pieces to p”
Contracting elements and random walks (2011, methodology): “bolic) with respect to the glued copies of ( H i) R. This can be easily proven using the denition of asymptotic tree-gradedness in terms of asymptotic cones [DS]. Alternatively, one can apply either [MR] or [Si1, Thereom 0.2] (see the proof of [Si1, Corollary 5.31]). Recall that any hyperbolic eleme”