TY - JOUR
T1 - Hybrid lattices and thin subgroups of Picard modular groups
AU - Paupert, Julien
AU - Wells, Joseph
N1 - Funding Information:
Both authors partially supported by National Science Foundation Grant DMS-1708463.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
KW - Complex hyperbolic geometry
KW - Discrete groups
KW - Lattices
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U2 - 10.1016/j.topol.2019.106918
DO - 10.1016/j.topol.2019.106918
M3 - Article
AN - SCOPUS:85074470572
SN - 0166-8641
VL - 269
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 106918
ER -