Discrete groups and the complex contact geometry of $Sl(2,\mathbb {C})$
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- by Brendan Foreman PDF
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Abstract:
We investigate the vertical foliation of the standard complex contact structure on $\Gamma \setminus Sl(2,\mathbb {C})$, where $\Gamma$ is a discrete subgroup. We find that, if $\Gamma$ is nonelementary, the vertical leaves on ${\Gamma }\setminus Sl(2,\mathbb {C})$ are holomorphic but not regular. However, if $\Gamma$ is Kleinian, then $\Gamma \setminus Sl(2,\mathbb {C})$ contains an open, dense set on which the vertical leaves are regular, complete and biholomorphic to $\mathbb {C}^*$. If $\Gamma$ is a uniform lattice, the foliation is nowhere regular, although there are both infinitely many compact and infinitely many nonclosed leaves.References
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Additional Information
- Brendan Foreman
- Affiliation: Department of Mathematics, John Carroll University, University Heights, Ohio 44118
- Received by editor(s): March 20, 2008
- Published electronically: February 12, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 4191-4200
- MSC (2000): Primary 32M05; Secondary 11E57, 30F40, 57R17
- DOI: https://doi.org/10.1090/S0002-9947-10-04972-X
- MathSciNet review: 2608401