An infinite-rank summand of knots with trivial Alexander polynomial
نویسندگان
چکیده
منابع مشابه
On Knots with Trivial Alexander Polynomial
We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which don’t have a Seifert surface whose genus equals the rank of the Seifert form. This is one of the first applications of the Kontsevich integral to intrinsically 3-dimensional questions in topology. Our examples contradict a lemma of Mike Freedman, and we explain what went...
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We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by ζ meaning an analogy with ζ-polynomial for virtual links. A degree of ζ-polynomial estimates a virtual crossing number. We describe some application of ζpolynomial for the study of minimal long virtual diagrams with respect number of virtual crossings. Virtual knot th...
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We show that given n > 0, there exists a hyperbolic knot K with trivial Alexander polynomial, trivial finite type invariants of orders ≤ n and such that the volume of the complement of K is larger than n. We compare our result with known results about the relation of hyperbolic volume and Alexander polynomials of alternating knots. We also discuss how our result compares with relations between ...
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ژورنال
عنوان ژورنال: Journal of Symplectic Geometry
سال: 2018
ISSN: 1527-5256,1540-2347
DOI: 10.4310/jsg.2018.v16.n6.a5