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

2015/09/07 by Alex Casella, Feng Luo, Casella, Alex +3
Mathematics · #57M25 #57N10 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1509.02233

openalex publication_date 2015/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalise work of Young-Eun Choi to the setting of ideal triangulations\nwith vertex links of arbitrary genus, showing that the set of all (possibly\nincomplete) hyperbolic cone-manifold structures realised by positively oriented\nhyperbolic ideal tetrahedra on a given topological ideal triangulation and with\nprescribed cone angles at all edges is (if non-empty) a smooth complex manifold\nof dimension the sum of the genera of the vertex links. Moreover, we show that\nthe complex lengths of a collection of peripheral elements give a local\nholomorphic parameterisation of this manifold.\n

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