FUNDAMENTAL DOMAINS FOR LATTICES IN RANK ONE SEMISIMPLE LIE GROUPS

Abstract

We construct a fundamental domain ω for an arbitrary lattice [unk] in a real rank one, real simple Lie group, where ω has finitely many cusps (i.e., is a finite union of Siegel sets) and has the Siegel property (i.e., the set {γ [unk] [unk]|ωγ [unk] ω [unk] ϕ} is finite). From the existence of ω we derive a number of consequences. In particular, we show that [unk] is finitely presentable and is almost always rigid.

Locations

• Proceedings of the National Academy of Sciences - View
• PubMed Central - View
• Europe PMC (PubMed Central) - View - PDF
• PubMed - View