INVERTIBLE KNOT CONCORDANCES AND PRIME KNOTS
نویسندگان
چکیده
منابع مشابه
Combinatorial Knot Contact Homology and Transverse Knots
We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial. We provide a number of computations of transverse homology that demonstrate its effectiv...
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Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S3. We will prove this conjecture for null-homologous knots in arbitrary closed 3-manifolds. Namely, if K is a knot in a closed 3-manifold Y , Y −K is irreducible, and ̂ HFK(Y, K ) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsváth–Szabó, Ghiggini and the author. A corollary is that i...
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For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which we can see small trefoil and figure-eight su...
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ژورنال
عنوان ژورنال: Honam Mathematical Journal
سال: 2010
ISSN: 1225-293X
DOI: 10.5831/hmj.2010.32.1.157