Shrinking simplicial subdivisions, strong barycenters, and limit sets of codimension one quasiconvex subgroups
Abstract
We show that quasiconvex subgroups of negatively curved manifold groups with codimension one have nicely embedded limit sets in the visual boundary if the complement of the limit sets admits what we call strong barycenters, a property related to the absence of large diameter sets with 'positive curvature.' Furthermore, we show that the same result can be obtained if, in the complement of the limit set, simplicial complexes can be subdivided in a way that 'shrinks' them metrically. This provides us with two sufficient geometric conditions for the limit set of a quasiconvex subgroup to be nicely embedded.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.05302
 Bibcode:
 2021arXiv210905302B
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory;
 Mathematics  Metric Geometry;
 51FXX;
 20F65;
 57N65
 EPrint:
 32 pages, 1 figure. Comments welcome!