Bounds on numerical boundary slopes for Montesinos knots
نویسندگان
چکیده
منابع مشابه
Boundary Slopes for Montesinos Knots
FOR A KNOT K c S3, let S(K) c Q u {CQ} be the set of slopes of boundary curves of incompressible, %incompressible orientable surfaces in the knot exterior, slopes being normalized in the standard way so that a longitude has slope 0, a meridian slope co. These sets S(K) of %slopes are of special interest because of their relation with Dehn surgery and character varieties; see e.g., [2]. The only...
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This note corrects errors in Hatcher and Oertel’s table of boundary slopes of Montesinos knots which have projections with 10 or fewer crossings.
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Exceptional Dehn surgeries on arborescent knots have been classified except for Seifert fibered surgeries on Montesinos knots of length 3. There are infinitely many of them as it is known that 4n + 6 and 4n + 7 surgeries on a (−2, 3, 2n + 1) pretzel knot are Seifert fibered. It will be shown that there are only finitely many others. A list of 20 surgeries will be given and proved to be Seifert ...
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Using the Hatcher–Oertel algorithm for finding boundary slopes of Montesinos knots, we prove the Slope Conjecture and the Strong Slope Conjecture for a family of 3-tangle pretzel knots. More precisely, we prove that the maximal degrees of the colored Jones polynomial of such a knot determine a boundary slope as predicted by the Slope Conjecture, and that the linear terms in the degrees correspo...
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A slope p q is called a characterizing slope for a given knot K0 in S if whenever the p q –surgery on a knot K in S is homeomorphic to the p q –surgery on K0 via an orientation preserving homeomorphism, then K D K0 . In this paper we try to find characterizing slopes for torus knots Tr;s . We show that any slope p q which is larger than the number 30.r 1/.s 1/=67 is a characterizing slope for T...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 2007
ISSN: 0018-2079
DOI: 10.32917/hmj/1187916319