Totally geodesic Seifert surfaces in hyperbolic knot and link complements II

Colin Adams; Hanna Bennett; Christopher James Davis; Michael Jennings; Jennifer Novak; Nicholas Perry; Eric Schoenfeld

Totally geodesic Seifert surfaces in hyperbolic knot and link complements II

Colin Adams, Hanna Bennett, Christopher James Davis, Michael Jennings, Jennifer Novak, Nicholas Perry, Eric Schoenfeld

Institut for Matematiske Fag

7 Citationer (Scopus)

Abstract

We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.

Originalsprog	Engelsk
Tidsskrift	Journal of Differential Geometry
Vol/bind	79
Udgave nummer	1
Sider (fra-til)	1-23
ISSN	0022-040X
Status	Udgivet - 2008

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Citationsformater

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abstract = "We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.",

author = "Colin Adams and Hanna Bennett and Davis, {Christopher James} and Michael Jennings and Jennifer Novak and Nicholas Perry and Eric Schoenfeld",

year = "2008",

language = "English",

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journal = "Journal of Differential Geometry",

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TY - JOUR

T1 - Totally geodesic Seifert surfaces in hyperbolic knot and link complements II

AU - Adams, Colin

AU - Bennett, Hanna

AU - Davis, Christopher James

AU - Jennings, Michael

AU - Novak, Jennifer

AU - Perry, Nicholas

AU - Schoenfeld, Eric

PY - 2008

Y1 - 2008

N2 - We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.

AB - We generalize the results of Adams–Schoenfeld, finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each covering a rigid 2-orbifold embedded in some hyperbolic 3-orbifold. In addition, we provide a uniqueness theorem and demonstrate that many knots cannot possess totally geodesic Seifert surfaces by giving bounds on the width invariant in the presence of such a surface. Finally, we utilize these examples to demonstrate that the Six Theorem is sharp for knot complements in the 3-sphere.

M3 - Journal article

SN - 0022-040X

VL - 79

SP - 1

EP - 23

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

ER -

Totally geodesic Seifert surfaces in hyperbolic knot and link complements II

Abstract

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