The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces

Autor:	Arana-Herrera, Francisco, Wright, Alex
Rok vydání:	2024
Předmět:	Mathematics - Geometric Topology Mathematics - Dynamical Systems Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	We prove a semi-simplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of totally geodesic subvarieties of moduli spaces of Riemann surfaces. Phrased at the level of Teichm\"uller space, this semi-simplicity theorem gives that each component of the boundary is a product of simple factors, each of which behaves metrically like a diagonal embedding. We use this to show that the associated totally geodesic submanifolds of Teichm\"uller space and orbifold fundamental groups are hierarchically hyperbolic. Comment: 46 pages; comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.16330 Zobrazit plný text záznamu View this record from Arxiv