Hyperbolic L-space knots and exceptional Dehn surgeries

Motegi, Kimihiko; Tohki, Kazushige

doi:10.1142/s0218216514500795

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…In this section, we verify that K 1 and K 2 admit positive Dehn surgeries yielding L-spaces by using the Montesinos trick [24]. For a surgery diagram on a strongly invertible link, the Montesinos trick describes the resulting closed 3-manifold as the double branched cover of another knot or link obtained from tangle replacements corresponding to the surgery coefficients on some link obtained from the quotient of the original strongly invertible link under the strong involution (see also [26,41]).…”

Section: The Montesinos Trickmentioning

confidence: 99%

Hyperbolic L-space knots and their formal semigroups

Teragaito

2022

Int. J. Math.

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For an L-space knot, the formal semigroup is defined from its Alexander polynomial. It is not necessarily a semigroup. That is, it may not be closed under addition. There exists an infinite family of hyperbolic L-space knots whose formal semigroups are semigroups generated by three elements. In this paper, we give the first infinite family of hyperbolic L-space knots whose formal semigroups are semigroups generated by five elements.

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Section: The Montesinos Trickmentioning

confidence: 99%

Hyperbolic L-space knots and their formal semigroups

Teragaito

2022

Int. J. Math.

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“…In recent years, work by many researchers provided insight on the fiberedness [Ni07,Ghi08], positivity [Hed10], and various notions of simplicity of L-space knots [OS05b,Hed11,Krc14]. For more examples of L-space knots, see [Hom11,Hom16,HLV14,Mot16,MT14,Vaf15].…”

Section: Introductionmentioning

confidence: 99%

On L-space knots obtained from unknotting arcs in alternating diagrams

Donald¹,

McCoy²,

Vafaee³

2016

Preprint

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Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S 3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD ∈ D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.Definition 1.2. Let (D, c) be an alternating diagram with an unknotting crossing c. Let C be a Conway sphere in D, disjoint from the unknotting arc specified by c. We will call the component of 1 An L-space Y is a rational homology sphere with the simplest possible Heegaard Floer invariant, that is rk HF (Y ) = |H1(Y ; Z)|.

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Exceptional Dehn Surgeries on Some Infinite Series of Hyperbolic Knots and Links

Cavicchioli,

Spaggiari

2024

Mediterr. J. Math.

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We study closed connected orientable 3-manifolds obtained by Dehn surgery along the oriented components of a link, introduced and considered by Motegi and Song (2005) and Ichihara et al. (2008). For such manifolds, we find a finite balanced group presentation of the fundamental group and describe exceptional surgeries. This allows us to construct an infinite family of tunnel number one strongly invertible hyperbolic knots with three parameters, which admit toroidal surgeries and Seifert fibered surgeries. Among the obtained results, we mention that for every integer $$n >5$$ n > 5 there are infinitely many hyperbolic knots in the 3–sphere, whose $$(n-2)$$ ( n - 2 ) and $$(n+1)$$ ( n + 1 ) -surgeries are toroidal, and $$(n-1)$$ ( n - 1 ) and n-surgeries are Seifert fibered.

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Hyperbolic L-space knots and exceptional Dehn surgeries

Cited by 3 publications

References 13 publications

Hyperbolic L-space knots and their formal semigroups

Hyperbolic L-space knots and their formal semigroups

On L-space knots obtained from unknotting arcs in alternating diagrams

Exceptional Dehn Surgeries on Some Infinite Series of Hyperbolic Knots and Links

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