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Conference Papers Year : 2022

Localized Geometric Moves to Compute Hyperbolic Structures on Triangulated 3-Manifolds

Clément Maria
  • Function : Author
  • PersonId : 926304
  • IdHAL : cmaria
Owen Rouillé
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  • PersonId : 1202214
  • IdRef : 26646565X

Abstract

A fundamental way to study 3-manifolds is through the geometric lens, one of the most prominent geometries being the hyperbolic one. We focus on the computation of a complete hyperbolic structure on a connected orientable hyperbolic 3-manifold with torus boundaries. This family of 3-manifolds includes the knot complements. This computation of a hyperbolic structure requires the resolution of gluing equations on a triangulation of the space, but not all triangulations admit a solution to the equations. In this paper, we propose a new method to find a triangulation that admits a solution to the gluing equations, using convex optimization and localized combinatorial modifications. It is based on Casson and Rivin’s reformulation of the equations. We provide a novel approach to modify a triangulation and update its geometry, along with experimental results to support the new method.
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Dates and versions

hal-03929416 , version 1 (08-01-2023)

Identifiers

  • HAL Id : hal-03929416 , version 1

Cite

Clément Maria, Owen Rouillé. Localized Geometric Moves to Compute Hyperbolic Structures on Triangulated 3-Manifolds. ESA 2022 - 30th Annual European Symposium on Algorithms, Sep 2022, Potsdam, Germany. ⟨hal-03929416⟩
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