Non-arithmetic hyperbolic orbifolds attached to unitary Shimura varieties

Olivier de Gaay Fortman

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arXiv · 2301.01598

Non-arithmetic hyperbolic orbifolds attached to unitary Shimura varieties

Olivier de Gaay Fortman

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Abstract

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.

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BibTeX RIS

Olivier de Gaay Fortman. 2023-01-04. Non-arithmetic hyperbolic orbifolds attached to unitary Shimura varieties. https://arxiv.org/abs/2301.01598

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