منابع مشابه
Concordance of links with identical Alexander invariants
Davis showed that the topological concordance class of a link in the 3-sphere is uniquely determined by its Alexander polynomial for 2-component links with Alexander polynomial one. A similar result for knots with Alexander polynomial one was shown earlier by Freedman. We prove that these two cases are the only exceptional cases, by showing that the link concordance class is not determined by t...
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This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney...
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We determine for which complex numbers on the unit circle the Levine-Tristram signature and the nullity give rise to link concordance invariants. 2010 Mathematics Subject Classification: primary: 57M25, secondary: 57M27, 57N70
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X iv :q -a lg /9 50 60 02 v2 3 1 Ju l 1 99 5 Abstract. The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given. The quantum group Uq(sl2), which gives rise to the Jones polynomial, is constructed explicitly. The 3-m...
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The extended Alexander group of an oriented virtual link l of d components is defined. From its abelianization a sequence of polynomial invariants ∆i(u1, . . . , ud, v), i = 0, 1, . . . , is obtained. When l is a classical link, ∆i reduces to the well-known ith Alexander polynomial of the link in the d variables u1v, . . . , udv; in particular, ∆0 vanishes.
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2012
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2012.12.2069