Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds
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- by Alex Casella, Feng Luo and Stephan Tillmann PDF
- Proc. Amer. Math. Soc. 145 (2017), 3543-3560 Request permission
Abstract:
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescribed cone angles at all edges is (if non-empty) a smooth complex manifold of dimension the sum of the genera of the vertex links. Moreover, we show that the complex lengths of a collection of peripheral elements give a local holomorphic parameterisation of this manifold.References
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Additional Information
- Alex Casella
- Affiliation: School of Mathematics and Statistics, The University of Sydney, NSW 2006 Australia
- MR Author ID: 1213818
- Email: casella@maths.usyd.edu.au
- Feng Luo
- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
- MR Author ID: 251419
- Email: fluo@math.rutgers.edu
- Stephan Tillmann
- Affiliation: School of Mathematics and Statistics, The University of Sydney, NSW 2006 Australia
- MR Author ID: 663011
- ORCID: 0000-0001-6731-0327
- Email: tillmann@maths.usyd.edu.au
- Received by editor(s): February 18, 2016
- Received by editor(s) in revised form: May 5, 2016, and May 11, 2016
- Published electronically: April 18, 2017
- Additional Notes: The first author was supported by a Commonwealth of Australia International Postgraduate Research Scholarship
The second author was partially supported by the United States National Science Foundation grants NSF DMS 1222663, 1207832, 1405106.
The third author was partially supported by Australian Research Council grant DP140100158 - Communicated by: David Futer
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3543-3560
- MSC (2010): Primary 57M25, 57N10
- DOI: https://doi.org/10.1090/proc/13290
- MathSciNet review: 3652806