Extensions of Veech groups II: Hierarchical hyperbolicity and quasiisometric rigidity
Abstract
We show that for any lattice Veech group in the mapping class group $\mathrm{Mod}(S)$ of a closed surface $S$, the associated $\pi_1 S$extension group is a hierarchically hyperbolic group. As a consequence, we prove that any such extension group is quasiisometrically rigid.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.00685
 arXiv:
 arXiv:2111.00685
 Bibcode:
 2021arXiv211100685D
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory;
 20F67;
 20F65;
 30F60;
 57M60;
 57M07
 EPrint:
 57 pages, 7 figures. This is the sequel to arXiv:2006.16425, which has now been divided into two parts. This part consists of the second half of the original version arXiv:2006.16425v1, along with the expanded and improved results that extensions of Veech groups are hierarchically hyperbolic groups and are quasiisometrically rigid