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A note on strong geometric isolation in 3-orbifolds

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arxiv math/0011126 v1 pith:65HK4YWM submitted 2000-11-17 math.GT

Danny Calegari This is my paper · ORCID
classification math.GT
keywords cuspsgeometricallyhyperbolicisolatedorbifoldorbifoldsamusingconjectured
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Neumann and Reid described in their paper "Rigidity of cusps in deformations of hyperbolic 3-orbifolds" (Math Ann. 295 (1993) no. 2, 223--237) a 2-cusped hyperbolic 3-orbifold in which the cusps are geometrically isolated. Based on numerical evidence provided by Jeff Weeks' snappea program, they conjectured that the cusps are strongly geometrically isolated, a fact which we establish here. We also give a parameterization of the Dehn surgery space of this orbifold which has amusing properties.

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  1. Expansion joints in hyperbolic manifolds

    math.GT 2025-11 conditional novelty 7.0 of 10

    Cone-deforming an ideal arc through 'expansion joints' interpolates between stacked Borromean ring complements and lantern manifolds, and yields cone deformations of highly twisted 2-bridge unknotting tunnels.

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