Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric 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 quasi-isometrically rigid.
- Publication:
-
arXiv e-prints
- 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
- E-Print:
- 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 quasi-isometrically rigid