Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere
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- by Irene Pasquinelli
- Conform. Geom. Dyn. 20 (2016), 235-281
- DOI: https://doi.org/10.1090/ecgd/299
- Published electronically: July 19, 2016
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Abstract:
Deligne and Mostow constructed a class of lattices in $PU(2,1)$ using monodromy of hypergeometric functions. Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for the lattices with three fold symmetry in the list of Deligne and Mostow. This is a generalisation of the works of Boadi and Parker and gives a different interpretation of the fundamental domain constructed by Deraux, Falbel, and Paupert.References
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Bibliographic Information
- Irene Pasquinelli
- Affiliation: Department of Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, United Kingdom
- Email: irene.pasquinelli@durham.ac.uk
- Received by editor(s): October 8, 2015
- Received by editor(s) in revised form: April 4, 2016
- Published electronically: July 19, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Conform. Geom. Dyn. 20 (2016), 235-281
- MSC (2010): Primary 32M05, 57M50, 51M10
- DOI: https://doi.org/10.1090/ecgd/299
- MathSciNet review: 3522983