Montesinos knots, hopf plumbings, and L-space surgeries

Kenneth Baker, Allison H. Moore

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Using Hirasawa–Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S3. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.

Original languageEnglish (US)
Pages (from-to)95-110
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume70
Issue number1
DOIs
StatePublished - Jan 1 2018

Fingerprint

L-space
Surgery
Knot
Fibered Knot
Tunnel
Classify
Tangles
Contact Structure
Decompose

Keywords

  • Fibered knot
  • L-space knot
  • Montesinos knot

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Montesinos knots, hopf plumbings, and L-space surgeries. / Baker, Kenneth; Moore, Allison H.

In: Journal of the Mathematical Society of Japan, Vol. 70, No. 1, 01.01.2018, p. 95-110.

Research output: Contribution to journalArticle

@article{17ac7ce2013548d1be1a0436901fe103,
title = "Montesinos knots, hopf plumbings, and L-space surgeries",
abstract = "Using Hirasawa–Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S3. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.",
keywords = "Fibered knot, L-space knot, Montesinos knot",
author = "Kenneth Baker and Moore, {Allison H.}",
year = "2018",
month = "1",
day = "1",
doi = "10.2969/jmsj/07017484",
language = "English (US)",
volume = "70",
pages = "95--110",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "1",

}

TY - JOUR

T1 - Montesinos knots, hopf plumbings, and L-space surgeries

AU - Baker, Kenneth

AU - Moore, Allison H.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Using Hirasawa–Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S3. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.

AB - Using Hirasawa–Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S3. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.

KW - Fibered knot

KW - L-space knot

KW - Montesinos knot

UR - http://www.scopus.com/inward/record.url?scp=85041902234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041902234&partnerID=8YFLogxK

U2 - 10.2969/jmsj/07017484

DO - 10.2969/jmsj/07017484

M3 - Article

VL - 70

SP - 95

EP - 110

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -