Non-arithmetic hyperbolic orbifolds attached to unitary Shimura varieties
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910727539785728 |
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| author | Fortman, Olivier de Gaay |
| author_facet | Fortman, Olivier de Gaay |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01598 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-arithmetic hyperbolic orbifolds attached to unitary Shimura varieties Fortman, Olivier de Gaay Geometric Topology Algebraic Geometry Group Theory Number Theory 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. |
| title | Non-arithmetic hyperbolic orbifolds attached to unitary Shimura varieties |
| topic | Geometric Topology Algebraic Geometry Group Theory Number Theory |
| url | https://arxiv.org/abs/2301.01598 |