منابع مشابه
Intersection Alexander polynomials
By considering a (not necessarily locally-flat) PL knot as the singular locus of a PL stratified pseudomanifold, we can use intersection homology theory to define intersection Alexander polynomials, a generalization of the classical Alexander polynomial invariants for smooth or PL locally-flat knots. We show that the intersection Alexander polynomials satisfy certain duality and normalization c...
متن کاملAlexander-Lin twisted polynomials
X.S. Lin’s original definition of twisted Alexander knot polynomial is generalized for arbitrary finitely presented groups. J. Cha’s fibering obstruction theorem is generalized. The group of a nontrivial virtual knot shown by L. Kauffman to have trivial Jones polynomial is seen also to have a faithful representation that yields a trivial twisted Alexander polynomial.
متن کاملMahler Measure of Alexander Polynomials
Let l be an oriented link of d components in a homology 3-sphere. For any nonnegative integer q, let l(q) be the link of d−1 components obtained from l by performing 1/q surgery on its dth component ld. The Mahler measure of the multivariable Alexander polynomial ∆l(q) converges to the Mahler measure of ∆l as q goes to infinity, provided that ld has nonzero linking number with some other compon...
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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 کاملBlock intersection polynomials
We introduce the block intersection polynomial, which is constructed using certain information about a block design with respect to a subset S of its point-set, and then provides further information about the number of blocks intersecting S in exactly i points, for i = 0, . . . , |S|. We also discuss some applications of block intersection polynomials, including bounding the multiplicity of a b...
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ژورنال
عنوان ژورنال: Topology
سال: 2004
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(03)00030-2