Hyperbolic groups with boundary an n-dimensional Sierpinski space
Geometric Topology
2019-03-05 v1 Group Theory
Abstract
For n>6, we show that if G is a torsion-free hyperbolic group whose visual boundary is an (n-2)-dimensional Sierpinski space, then G=\pi_1(W) for some aspherical n-manifold W with nonempty boundary. Concerning the converse, we construct, for each n>3, examples of aspherical manifolds with boundary, whose fundamental group G is hyperbolic, but with visual boundary not homeomorphic to an (n-2)-dimensional Sierpinski space.
Cite
@article{arxiv.1505.03817,
title = {Hyperbolic groups with boundary an n-dimensional Sierpinski space},
author = {Jean-François Lafont and Bena Tshishiku},
journal= {arXiv preprint arXiv:1505.03817},
year = {2019}
}
Comments
11 pages