Alexander polynomials of equivariant slice and ribbon knots in $S^3$
نویسندگان
چکیده
منابع مشابه
On Equivariant Slice Knots
We suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots — Naik’s and Choi-Ko-Song’s improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots — but are not equivariantly slice. Introduction An oriented ...
متن کاملOn Equivariant Slice Knots
We suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots— Naik’s and Choi-Ko-Song’s improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots — but are not equivariantly slice.
متن کاملAlexander Polynomials of Ribbon Links
We give a simple argument to show that every polynomial f(t) ∈ Z[t] such that f(1) = 1 is the Alexander polynomial of some ribbon 2-knot whose group is a 1-relator group, and we extend this result to links. It is well known that every Laurent polynomial f(t) ∈ Λ = Z[t, t] with f(1) = 1 is the Alexander polynomial of some ribbon 2-knot [7]. (See also [1, 2], for the fibred case, and §7H of [11],...
متن کاملNontrivial Alexander Polynomials of Knots and Links
In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguishing knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial knots. Furthermore we prove that these invariants decide if a genus one knot ...
متن کاملAlexander polynomials of non-locally-flat knots
We generalize the classical study of Alexander polynomials of smooth or PL locally-flat knots to PL knots that are not necessarily locally-flat. We introduce three families of generalized Alexander polynomials and study their properties. For knots with point singularities, we obtain a classification of these polynomials that is complete except for one special low-dimensional case. This classifi...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03741-4