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Pseudo-developing maps for ideal triangulations II: Positively oriented ideal triangulations of cone-manifolds


Authors: Alex Casella, Feng Luo and Stephan Tillmann
Journal: Proc. Amer. Math. Soc. 145 (2017), 3543-3560
MSC (2010): Primary 57M25, 57N10
DOI: https://doi.org/10.1090/proc/13290
Published electronically: April 18, 2017
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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.


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Additional Information

Alex Casella
Affiliation: School of Mathematics and Statistics, The University of Sydney, NSW 2006 Australia
Email: casella@maths.usyd.edu.au

Feng Luo
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
Email: fluo@math.rutgers.edu

Stephan Tillmann
Affiliation: School of Mathematics and Statistics, The University of Sydney, NSW 2006 Australia
Email: tillmann@maths.usyd.edu.au

DOI: https://doi.org/10.1090/proc/13290
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
Article copyright: © Copyright 2017 American Mathematical Society