COMMENSURABILITY CLASSES OF TWIST KNOTS
نویسندگان
چکیده
منابع مشابه
Commensurability Classes of Twist Knots
In this paper we prove that if MK is the complement of a non-fibered twist knot K in S, then MK is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In ad...
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In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m(52) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston–Bennequin number of the twist knot K−2n with crossing number 2n+1. In this paper we give a complete classification of Legendrian and transverse representatives o...
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Litherland has shown that if a knot is (+)-amphicheiral then its m-twist-spin is reversible. We show that, for classical knots, in many cases the converse holds. The irreversibility (sometimes called noninvertibility) of certain twist-spun knots has been established by Ruberman [10], using the Farber-Levine linking pairing and the Casson-Gordon invariants. More recently, alternative proofs of t...
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We study representations of the knot groups of twist knots into SL2(C). The set of nonabelian SL2(C) representations of a twist knot K is described as the zero set in C × C of a polynomial PK(x, y) = QK(y) + xRK(y) ∈ Z[x, y], where x is the trace of a meridian. We prove some properties of PK(x, y). In particular, we prove that PK(2, y) ∈ Z[y] is irreducible over Q. As a consequence, we obtain a...
متن کاملWhich Finite Simple Knots Are Twist-spun?
We investigate which simple even-dimensional knots with finite knot modules may arise as twist-spun simple knots; and give some examples of knots which cannot so arise for reasons which are essentially number-theoretic.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2005
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216505003737