Alexander polynomials of links of small order
نویسندگان
چکیده
منابع مشابه
Alexander 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 کاملOn Alexander-Conway polynomials of two-bridge links
We consider Conway polynomials of two-bridge links as Euler continuant polynomials. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley on Alexander polynomials. We give a modulo 2 congruence for links, which implies the classical modulo 2 Murasugi congruence for knots. We also give sharp bounds for the coefficients of the Conway and Alexander polynomials...
متن کاملOn Alexander-conway Polynomials for Virtual Knots and Links
A polynomial invariant of virtual links, arising from an invariant of links in thickened surfaces introduced by Jaeger, Kauuman, and Saleur, is deened and its properties are investigated. Examples are given that the invariant can detect chirality and even non-invertibility of virtual knots and links. Furthermore, it is shown that the polynomial satisses a Conway-type skein relation { in contras...
متن کاملThe Jones and Alexander polynomials for singular links
We extend the Kauffman state models of the Jones and Alexander polynomials of classical links to state models of their two-variable extensions in the case of singular links. Moreover, we extend both of them to polynomials with d+1 variables for long singular knots with exactly d double points. These extensions can detect non-invertibility of long singular knots. 1
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1978
ISSN: 0019-2082
DOI: 10.1215/ijm/1256048608