Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties
Abstract
We construct non-arithmetic lattices in $PO(n,1)$ for each integer $n$ greater than one. To do so, we provide a construction of glueing together complete real hyperbolic orbifolds along totally geodesic subspaces. The hyperbolic orbifolds that we glue are those that arise from anti-unitary involutions on a unitary Shimura variety. This construction generalizes a method of Allcock-Carlson-Toledo, who glued hyperbolic quotient spaces in dimensions two, three and four.
Domains
Geometric Topology [math.GT]
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