Small knot complements, exceptional surgeries and hidden symmetries

Neil R. Hoffman

doi:10.2140/agt.2014.14.3227

Small knot complements, exceptional surgeries and hidden symmetries

Neil R. Hoffman

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

5 Scopus citations

Abstract

This paper provides two obstructions to small knot complements in S³ admitting hidden symmetries. The first obstruction is being cyclically commensurable with another knot complement. This result provides a partial answer to a conjecture of Boileau, Boyer, Cebanu and Walsh. We also provide a second obstruction to admitting hidden symmetries in the case where a small knot complement covers a manifold admitting some symmetry and at least two exceptional surgeries.

Original language	English (US)
Pages (from-to)	3227-3258
Number of pages	32
Journal	Algebraic and Geometric Topology
Volume	14
Issue number	6
DOIs	https://doi.org/10.2140/agt.2014.14.3227
State	Published - Jan 15 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2014 Mathematical Sciences Publishers. All rights reserved.

Keywords

Commensurability
Exceptional surgeries
Hidden symmetries
Knot complements
Trace field

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10.2140/agt.2014.14.3227

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AB - This paper provides two obstructions to small knot complements in S3 admitting hidden symmetries. The first obstruction is being cyclically commensurable with another knot complement. This result provides a partial answer to a conjecture of Boileau, Boyer, Cebanu and Walsh. We also provide a second obstruction to admitting hidden symmetries in the case where a small knot complement covers a manifold admitting some symmetry and at least two exceptional surgeries.

KW - Commensurability

KW - Exceptional surgeries

KW - Hidden symmetries

KW - Knot complements

KW - Trace field

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Small knot complements, exceptional surgeries and hidden symmetries

Abstract

Bibliographical note

Keywords

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