منابع مشابه
Seifert forms and concordance
If a knot K has Seifert matrix VK and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non–concordant knots having Seifert matrix VK . AMS Classification numbers Primary: 57M25 Secondary: 57N70
متن کاملEXAMPLES IN CONCORDANCE 3 Seifert
In this paper we present a series of examples of new phenomena in the classical knot concordance group. First we show that for (almost) every Seifert form there is an infinite family of knots, distinct in concordance, having that form. Next we demonstrate that a number of results that are known to hold in higher dimensional concordance fail in the classical case. These include: (1) examples of ...
متن کامل2nd Order Algebraic Concordance and Twisted Blanchfield Forms
In my first year report [16] I described how to write down explicitly the chain complex C∗(X̃) for the universal cover of the knot exterior X, given a knot diagram. In this report we describe work to fit this chain complex into an algebraic group which we construct which measures a “2nd order slice-ness obstruction,” in the sense that it obstructs the concordance class of a knot lying in the lev...
متن کاملUnknotting Tunnels and Seifert Surfaces
Let K be a knot with an unknotting tunnel γ and suppose that K is not a 2-bridge knot. There is an invariant ρ = p/q ∈ Q/2Z, p odd, defined for the pair (K, γ). The invariant ρ has interesting geometric properties: It is often straightforward to calculate; e. g. for K a torus knot and γ an annulus-spanning arc, ρ(K, γ) = 1. Although ρ is defined abstractly, it is naturally revealed when K ∪ γ i...
متن کاملSeifert circles and knot polynomials
In this paper I shall show how certain bounds on the possible diagrams presenting a given oriented knot or link K can be found from its two-variable polynomial PK defined in [3]. The inequalities regarding exponent sum and braid index of possible representations of K by a closed braid which are proved in [5] and [2] follow as a special case. Notation. In a diagram D for an oriented knot, write ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2002
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2002.6.403