ON THE REVERSIBILITY OF TWIST-SPUN KNOTS
نویسندگان
چکیده
منابع مشابه
On the Reversibility of Twist-spun Knots
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 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.
متن کاملTwisting Spun Knots
1. Introduction. In [5] Mazur constructed a homotopy 4-sphere which looked like one of the strongest candidates for a counterexample to the 4-dimensional Poincaré Conjecture. In this paper we show that Mazur's example is in fact a true 4-sphere after all. This raises the odds in favour of the 4-dimensional Poincaré Conjecture. The proof involves a smooth knot of S2 in S4 with unusual properties.
متن کاملOn Nonabelian Representations of Twist Knots
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 کاملThere are two 2–twist-spun trefoils
We give a short proof inspired by Carter et al [1] that the 2–twist-spun trefoil is not isotopic to its orientation reverse. The proof uses a computer calculation of the third homology group of the three colour rack. We also give a new proof using the same calculation of the well-known fact that the left and right trefoil knots are not isotopic. AMS Classification 57Q45; 57M25, 57M27
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2003
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216503002822