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 language | English (US) |
|---|---|
| Pages (from-to) | 95-110 |
| Number of pages | 16 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 70 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2018 |
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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 journal › Article
}
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 -