2003
DOI: 10.32917/hmj/1150997871
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Longitudinal slope and Dehn fillings

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Cited by 14 publications
(14 citation statements)
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“…Therefore S 3 N (K) = Σ(L 1 )#Σ(L 2 ) is reducible. Using work of Hoffman, Matignon-Sayari showed that if S 3 N (K) is a reducible surgery, then either N ≤ 2g(K) − 1 or K is a cable knot [12,14]. Since we have…”
Section: 3mentioning
confidence: 95%
“…Therefore S 3 N (K) = Σ(L 1 )#Σ(L 2 ) is reducible. Using work of Hoffman, Matignon-Sayari showed that if S 3 N (K) is a reducible surgery, then either N ≤ 2g(K) − 1 or K is a cable knot [12,14]. Since we have…”
Section: 3mentioning
confidence: 95%
“…It is a theorem of Matignon and Sayari [52] that if S 3 n (K) is reducible for a non-cable K, then |n| ≤ 2g(K) − 1, where g(K) is the Seifert genus of K. Therefore, if tb(K) is large, this can strongly restrict the range of possible reducible surgeries on K. We illustrate this with positive knots. Theorem 1.7.…”
Section: 2mentioning
confidence: 96%
“…Proof. The cabling conjecture is true for genus 1 knots by [10] (see also [52,39]). If nsurgery on the genus 2 positive knot K is a counterexample then K must be hyperbolic by Theorem 2.1 (in particular, K is prime) and n = 2g(K) − 1 = 3 by Theorem 1.7.…”
Section: 2mentioning
confidence: 97%
“…Since S 3 r (K) must have a non-trivial lens space summand, the integral reducing slope r satisifes r = −1, 0, 1. In [MS03], Matignon and Sayari provide the following genus bound if K is non-cabled:…”
Section: Introductionmentioning
confidence: 99%