Dehn filling in relatively hyperbolic groups

By D. Groves, J. Manning. 2006

261 citations recorded by the source corpus.

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev.As an application, we prove a group-theoretic analog of the Gromov-Thurston 2π Theorem in the context of relatively hyperbolic groups.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/990611bdc3fcd087025557204ab3e5cee18a2d53

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

RESEARCH ANNOUNCEMENT: THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY (2009, background): “This work joins a variety of generalizations of small-cancellation theory including works of [38, 33, 39, 16].”
Residual finiteness, QCERF, and fillings of hyperbolic groups (2008, methodology): “We also assume, as in [8] that ı is an integer greater than or equal to 100.”
The virtual Haken conjecture (2012, background): “This does not change the coarse geometry of G or any of the statements we apply from [17, 1, 31, 23].”
Relative hyperbolicity and relative quasiconvexity for countable groups (2008, methodology): “The following result is proved by Groves{Manning under the additional hypothesis that (P;d) is the set of vertices of a connected metric graph where each edge has length one [ GM ,x3.1].”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, methodology): “As an illustration of this idea we generalize the group theoretic analogue of Thurston’s hyperbolic Dehn surgery theorem proved for relatively hyperbolic groups in [105] (see also [66]).”
On metric relative hyperbolicity (2012, background): “In fact, the horoballs as defined above are quasi-isometric to the combinatorial horoballs defined in [GM08].”
GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, result): “It was also independently proved by Groves and Manning [2008] under the additional assumptions that the group G is torsion free and finitely generated.”
Growth tight actions (2014, background): “5 [Bowditch 2012; Groves and Manning 2008; Sisto 2012].”
Asymptotic dimension and small‐cancellation for hierarchically hyperbolic spaces and groups (2015, background): “We begin by recalling from [18] the notion of a combinatorial horoball, and the attendant hyperbolic cone construction from [14].”
Stable commutator length in word-hyperbolic groups (2006, unknown): “[23], [31]).”
Acylindrically hyperbolic groups (2013, background): “It is not hard to show (see [22]) that the graph H(G) is always hyperbolic.”