scholarly journals Height, graded relative hyperbolicity and quasiconvexity

2017 ◽  
Vol 4 ◽  
pp. 515-556 ◽  
Author(s):  
François Dahmani ◽  
Mahan Mj
Keyword(s):  
Relative Hyperbolicity

scholarly journals Relative hyperbolicity, trees of spaces and Cannon-Thurston maps

2010 ◽  
Vol 151 (1) ◽  
pp. 59-78 ◽  
Author(s):  
Mahan Mj ◽  
Abhijit Pal
Keyword(s):  
Relative Hyperbolicity

scholarly journals Projections and relative hyperbolicity

2013 ◽  
Vol 59 (1) ◽  
pp. 165-181 ◽  
Author(s):  
Alessandro Sisto
Keyword(s):  
Relative Hyperbolicity

scholarly journals From Hierarchical to Relative Hyperbolicity

2020 ◽  
Author(s):  
Jacob Russell
Keyword(s):  
Hyperbolic Space ◽  
Teichmüller Space ◽  
Hyperbolic Groups ◽  
Teichmuller Space ◽  
Curve Graph ◽  
New Formulation ◽  
Relatively Hyperbolic ◽  
Relative Hyperbolicity

Abstract We provide a simple, combinatorial criteria for a hierarchically hyperbolic space to be relatively hyperbolic by proving a new formulation of relative hyperbolicity in terms of hierarchy structures. In the case of clean hierarchically hyperbolic groups, this criteria characterizes relative hyperbolicity. We apply our criteria to graphs associated to surfaces and prove that the separating curve graph of a surface is relatively hyperbolic when the surface has zero or two punctures. We also recover a celebrated theorem of Brock and Masur on the relative hyperbolicity of the Weil–Petersson metric on Teichmüller space for surfaces with complexity three.

scholarly journals An obstruction to the strong relative hyperbolicity of a group

2007 ◽  
Vol 10 (6) ◽  
Author(s):  
James W Anderson ◽  
Javier Aramayona ◽  
Kenneth J Shackleton
Keyword(s):  
Relative Hyperbolicity

scholarly journals A Note on Fine Graphs and Homological Isoperimetric Inequalities

2016 ◽  
Vol 59 (01) ◽  
pp. 170-181 ◽  
Author(s):  
Eduardo Martínez-Pedroza
Keyword(s):  
Isoperimetric Inequality ◽  
Isoperimetric Inequalities ◽  
Positive Answer ◽  
Cell Complex ◽  
Conjugacy Classes ◽  
Homological Characterization ◽  
Simply Connected ◽  
Relative Hyperbolicity ◽  
Dimensional Cell

Abstract In the framework of homological characterizations of relative hyperbolicity, Groves and Manning posed the question of whether a simply connected 2-complex X with a linear homological isoperimetric inequality, a bound on the length of attachingmaps of 2-cells, and finitely many 2-cells adjacent to any edge must have a fine 1-skeleton. We provide a positive answer to this question. We revisit a homological characterization of relative hyperbolicity and show that a group G is hyperbolic relative to a collection of subgroups P if and only if G acts cocompactly with ûnite edge stabilizers on a connected 2-dimensional cell complex with a linear homological isoperimetric inequality and P is a collection of representatives of conjugacy classes of vertex stabilizers.

scholarly journals Thickness, relative hyperbolicity, and randomness in Coxeter groups

2017 ◽  
Vol 17 (2) ◽  
pp. 705-740 ◽  
Author(s):  
Jason Behrstock ◽  
Mark Hagen ◽  
Alessandro Sisto
Keyword(s):  
Coxeter Groups ◽  
Relative Hyperbolicity

scholarly journals Invariance of coarse median spaces under relative hyperbolicity

2012 ◽  
Vol 154 (1) ◽  
pp. 85-95 ◽  
Author(s):  
BRIAN H. BOWDITCH
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Groups ◽  
Relative Hyperbolicity

AbstractWe show that, for finitely generated groups, the property of admitting a coarse median structure is preserved under relative hyperbolicity.

scholarly journals Relative hyperbolicity, classifying spaces, and lower algebraic K-theory

Topology ◽  
2007 ◽  
Vol 46 (6) ◽  
pp. 527-553 ◽  
Author(s):  
Jean-François Lafont ◽  
Ivonne J. Ortiz
Keyword(s):  
Classifying Spaces ◽  
Relative Hyperbolicity

scholarly journals Novikov Conjectures and Relative Hyperbolicity

1999 ◽  
Vol 85 (2) ◽  
pp. 169 ◽  
Author(s):  
Boris Goldfarb
Keyword(s):  
Symmetric Spaces ◽  
Large Family ◽  
Hyperbolic Groups ◽  
Fundamental Groups ◽  
Arithmetic Groups ◽  
Relatively Hyperbolic Groups ◽  
Rank One ◽  
Higher Rank ◽  
Relatively Hyperbolic ◽  
Relative Hyperbolicity

We consider a class of relatively hyperbolic groups in the sense of Gromov and use an argument modeled after Carlsson-Pedersen to prove Novikov conjectures for these groups. This proof is related to [16,17] which dealt with arithmetic lattices in rank one symmetric spaces and some other arithmetic groups of higher rank. Here whe view the rank one lattices in this different larger context of relativve hyperbolicity which also inclues fundamental groups of pinched hyperbolic manifolds. Another large family of groups from this class is produced using combinatorial hyperbolization techniques.

Sign in / Sign up

Export Citation Format

Share Document