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

Mathematics (Morris)

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

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

Publisher link

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.",

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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language = "English (US)",

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T1 - Guts and volume for hyperbolic 3-orbifolds with underlying space S3

AU - Atkinson, Chris

AU - Mallepalle, Jessica

AU - Melby, Joseph M.

AU - Rafalski, Shawn

AU - Vaccaro, Jennifer

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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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KW - 2-Dimensional suborbifold

KW - Essential annuli

KW - Guts

KW - Haken orbifold

KW - Hyperbolic 3-dimensional orbifold

KW - Hyperbolic orbifold

KW - Hyperbolic volume

KW - Incompressible 2-orbifold

KW - Orbifold annuli

KW - Pared acylindrical orbifold

KW - Rational tangle

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