Projections and relative hyperbolicity

By Alessandro Sisto. 2010

70 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7076332955f83779f38b7edbc88062b55bd5c26c

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quasi-convexity of hyperbolically embedded subgroups (2013, background): “ hyperbolic spaces are collected in the following lemma. The rst item is [DS05, Theorem 4.1-( 1)], while (stronger versions of) the other two can be deduced from results in [DS05] and can be found in [Sis13]. Lemma 2.3. Let X be a metric space hyperbolic relative to the collection of subsets P. For ”
On metric relative hyperbolicity (2012, methodology): “The uniform bound then follows from (AP ′2) in [Sis10].”
Hierarchically hyperbolic spaces I: curve complexes for cubical groups (2014, background): “tric space that is hyperbolic relative to a collectionofhierarchicallyhyperbolicsubspacesishierarchicallyhyperbolic[BHS]. Wenote thatitisalreadyknownthatrelativelyhyperbolicgroupsadmitadistanceformula[Sis13]. Anotherinterestingquestioniswhetheraright-angledArtingroupendowedwiththesyllable lengthmetr”
Hierarchically hyperbolic spaces II: Combination theorems and the distance formula (2015, background): “e inequality, it suces to consider UPS gP;V PS g 1P with gP˘g1P1. Let xPGand let z g g 1P pxq. Then, if d Upx;zqis suciently large, then d gPpx;zqis correspondingly large, so that by Lemma 1.15 of [Sis13], g g 1P pxqand g gP1pgPqcoarsely coincide, as desired. The last part of the consistency axiom, ”