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Mostow’s lattices and cone metrics on the sphere
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Richard K. Boadi
and
John R. Parker
Published/Copyright:
January 14, 2015
Abstract
In his seminal paper of 1980, Mostow constructed a family of lattices in PU(2, 1), the holomorphic isometry group of complex hyperbolic 2-space. In this paper, we use a description of these lattices given by Thurston in terms of cone metrics on the sphere, which is equivalent to Deligne and Mostow’s description of them using monodromy of hypergeometric functions. We give an explicit fundamental domain for some of Mostow’s lattices, specifically those with large phase shift. Our approach follows Parker’s approach of describing Livné’s lattices in terms of cone metrics on the sphere. The content of this paper is based on Boadi’s PhD thesis.
Received: 2013-1-16
Revised: 2013-5-14
Published Online: 2015-1-14
Published in Print: 2015-1-1
© 2015 by Walter de Gruyter Berlin/Boston
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- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
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- The topology of the minimal regular covers of the Archimedean tessellations
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Articles in the same Issue
- Frontmatter
- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
- Displacing (Lagrangian) submanifolds in the manifolds of full flags
- The harmonic mean measure of symmetry for convex bodies
- Geodesic vectors and subalgebras in two-step nilpotent metric Lie algebras
- The periods of the generalized Jacobian of a complex elliptic curve
