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 journalArticlepeer-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 languageEnglish (US)
    Pages (from-to)100-113
    Number of pages14
    JournalTopology and its Applications
    Volume243
    DOIs
    StatePublished - 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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