2,173 research outputs found
Quasi-actions on trees and Property (QFA)
We prove some general results about quasi-actions on trees and define
Property (QFA), which is analogous to Serre's Property (FA), but in the coarse
setting. This property is shown to hold for a class of groups, including
for . We also give a way of thinking about Property (QFA)
by breaking it down into statements about particular classes of trees.Comment: 23 pages, Appendix on "Boundedly generated groups with
pseudocharacter(s)" by Nicolas Monod and Bertrand R\'emy. References have
been updated. Some statements in Section 4 have been modifie
Dehn filling in relatively hyperbolic groups
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
2\pi Theorem in the context of relatively hyperbolic groups.Comment: 83 pages. v2: An improved version of preferred paths is given, in
which preferred triangles no longer need feet. v3: Fixed several small errors
pointed out by the referee, and repaired several broken figures. v4:
corrected definition 2.38. This is very close to the published versio
An alternate proof of Wise's Malnormal Special Quotient Theorem
We give an alternate proof of Wise's Malnormal Special Quotient Theorem
(MSQT), avoiding cubical small cancellation theory. We also show how to deduce
Wise's Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu--Wise
and Haglund--Wise.Comment: 42 pages, 10 figures. Version 2 contains minor changes, addressing
referee comments. To appear in Forum of Mathematics, P
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