Hybrid lattices and thin subgroups of Picard modular groups

Julien Paupert, Joseph Wells

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Abstract

We consider a certain hybridization construction which produces a subgroup of PU(n,1) from a pair of lattices in PU(n−1,1). Among the Picard modular groups PU(2,1,Od), we show that the hybrid of pairs of Fuchsian subgroups PU(1,1,Od) is a lattice when d=1 and d=7, and a geometrically infinite thin subgroup when d=3, that is an infinite-index subgroup with the same Zariski-closure as the full lattice.

Original languageEnglish (US)
Article number106918
JournalTopology and its Applications
Volume269
DOIs
Publication statusPublished - Jan 1 2020

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Keywords

  • Complex hyperbolic geometry
  • Discrete groups
  • Lattices

ASJC Scopus subject areas

  • Geometry and Topology

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