Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 5 Dec 2024 |
Abstract
Keywords
- math.GT, math.AG, math.GR, math.NT
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2024.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties
AU - de Gaay Fortman, Atahualpa Olivier Daniel
N1 - 39 pages. v3: remarks added in Section 1.2, concerning a comparison with the Gromov--Piatetski-Shapiro construction, and the volume of the constructed hyperbolic orbifolds
PY - 2024/12/5
Y1 - 2024/12/5
N2 - We develop a new method of constructing non-arithmetic lattices in the projective orthogonal group \(\text{PO}(n,1)\) for every integer \(n\) larger than one. The technique is to consider anti-holomorphic involutions on a complex arithmetic ball quotient, glue their fixed loci along geodesic subspaces, and show that the resulting metric space carries canonically the structure of a complete real hyperbolic orbifold. The volume of various of these non-arithmetic orbifolds can be explicitly calculated.
AB - We develop a new method of constructing non-arithmetic lattices in the projective orthogonal group \(\text{PO}(n,1)\) for every integer \(n\) larger than one. The technique is to consider anti-holomorphic involutions on a complex arithmetic ball quotient, glue their fixed loci along geodesic subspaces, and show that the resulting metric space carries canonically the structure of a complete real hyperbolic orbifold. The volume of various of these non-arithmetic orbifolds can be explicitly calculated.
KW - math.GT
KW - math.AG
KW - math.GR
KW - math.NT
M3 - Preprint
BT - Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties
ER -