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Conformal Geometry and Dynamics

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Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere


Author: Irene Pasquinelli
Journal: Conform. Geom. Dyn. 20 (2016), 235-281
MSC (2010): Primary 32M05, 57M50, 51M10
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.


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Additional 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

DOI: https://doi.org/10.1090/ecgd/299
Received by editor(s): October 8, 2015
Received by editor(s) in revised form: April 4, 2016
Published electronically: July 19, 2016
Article copyright: © Copyright 2016 American Mathematical Society