Abstract
AbstractWe prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.
Funder
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
National Science Foundation
Publisher
Springer Science and Business Media LLC
Reference15 articles.
1. Abert, M., Bergeron, N., Biringer, I., Gelander, T., Nikolov, N., Raimbault, J., Samet, I.: On the growth of $$L^2$$-invariants for sequences of lattices in Lie groups. Ann. of Math. (2) 185(3), 711–790 (2017)
2. Bader, U., Fisher, D., Miller, N., Stover, M.: Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds, (2020)
3. Bader, U., Fisher, D., Miller, N., Stover, M.: Arithmeticity, superrigidity, and totally geodesic submanifolds, (2019)
4. Corlette, K.: Archimedean superrigidity and hyperbolic geometry. Ann. Math. 135(1), 165–182 (1992)
5. Eskin, A., Mirzakhani, M.: Invariant and stationary measures for the $${\rm SL}(2,\mathbb{R})$$ action on moduli space. Publ. Math. Inst. Hautes Études Sci. 127, 95–324 (2018)