Guts and volume for hyperbolic 3-orbifolds with underlying space S3

Chris Atkinson; Jessica Mallepalle; Joseph M. Melby; Shawn Rafalski; Jennifer Vaccaro

doi:10.1016/j.topol.2018.05.004

Guts and volume for hyperbolic 3-orbifolds with underlying space S³

Chris Atkinson, Jessica Mallepalle, Joseph M. Melby, Shawn Rafalski, Jennifer Vaccaro

Research output: Contribution to journal › Article › peer-review

Abstract

Let O be a hyperbolic 3-orbifold with underlying space the 3-sphere. If O contains an essential 2-suborbifold with underlying space the 2-sphere with four cone points, we show how to compute the guts of O split along the 2-suborbifold. When the guts are non-empty, we obtain volume bounds in terms of the topology of the guts. When the guts are empty, we give a complete description of the topological structure of O.

Original language	English (US)
Pages (from-to)	100-113
Number of pages	14
Journal	Topology and its Applications
Volume	243
DOIs	https://doi.org/10.1016/j.topol.2018.05.004
State	Published - Jul 1 2018

Bibliographical note

Funding Information:
This work is supported by a grant from the National Science Foundation DMS-1358454 .

Funding Information:
The authors give special thanks to Ian Agol and Peter Shalen for helpful conversations. Much of the work in this paper was done as part of the 2015 Fairfield University REU Program, sponsored by the National Science Foundation.

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

2-Dimensional suborbifold
Essential annuli
Guts
Haken orbifold
Hyperbolic 3-dimensional orbifold
Hyperbolic orbifold
Hyperbolic volume
Incompressible 2-orbifold
Orbifold annuli
Pared acylindrical orbifold
Rational tangle

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10.1016/j.topol.2018.05.004

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Cite this

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title = "Guts and volume for hyperbolic 3-orbifolds with underlying space S3",

abstract = "Let O be a hyperbolic 3-orbifold with underlying space the 3-sphere. If O contains an essential 2-suborbifold with underlying space the 2-sphere with four cone points, we show how to compute the guts of O split along the 2-suborbifold. When the guts are non-empty, we obtain volume bounds in terms of the topology of the guts. When the guts are empty, we give a complete description of the topological structure of O.",

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AU - Mallepalle, Jessica

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AU - Rafalski, Shawn

AU - Vaccaro, Jennifer

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