Projections and relative hyperbolicity

2010/10/21 by Alessandro Sisto, Sisto, Alessandro · 6 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG) #math.GR #math.GT #math.MG

paper · pdf · doi:10.48550/arxiv.1010.4552

The previous version has been split, the present version is a revision of the first part of the old version. The second part is now called "Tree-graded asymptotic cones"

arxiv created 2012/04/03 · arxiv updated 2012/04/04

Abstract

We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class groups.

Cited by

• Largest acylindrical actions of free-by-cyclic groups
• Sublinear projection tracking in acylindrically hyperbolic groups
• On the almost sure spiraling of geodesics in CAT(0) spaces
• Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
• Central extensions and proper actions on products of hyperbolic spaces
• Tree-graded asymptotic cones

Related

• Relatively hyperbolic groups: geometry and quasi-isometric invariance
• The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups
• On metric relative hyperbolicity
• A recipe for constructing non-Hopfian relatively hyperbolic groups with Hopfian peripheral subgroups
• Peripheral structures of relatively hyperbolic groups