A note on 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...
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.
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 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
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...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1986-0848900-5