منابع مشابه
Knot Adjacency and Fibering
It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of knot adjacency can be used to obtain obstructions to fibering of knots and of 3-manifolds. As an application, given a fibered knot K′, we construct infinitely many non-fibered knots that share the...
متن کاملKnot Adjacency, Genus and Essential Tori
A knot K is called n-adjacent to another knot K , if K admits a projection containing n “generalized crossings” such that changing any 0 < m ≤ n of them yields a projection of K . We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to answer the question of the extent to which non-isotopic knots can be adjacent to each o...
متن کاملHigher Degree Knot Adjacency as Obstruction to Fibering
It is know that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of “knot adjacency”, studied in [KL], can be used to obtain obstructions to fibering of knots and of 3-manifolds. As an application, given a fibered knot K′, we construct infinitely many non-fibered k...
متن کاملAdjacency on Combinatorial Polyhedra
This paper shows some useful properties of the adjacency structures of a class of combinatorial polyhedra including the equality constrained 0-1 polytopes. The class of polyhedra considered here includes 0-1 polytopes related to some combinatorial optimization problems; e.g., set partitioning polytopes, set packing polytopes, perfect matching polytopes, vertex packing polytopes and all the face...
متن کاملOn Generalized Knot Groups
Generalized knot groups Gn(K) were introduced first by Wada and Kelly independently. The classical knot group is the first one G1(K) in this series of finitely presented groups. For each natural number n, G1(K) is a subgroup of Gn(K) so the generalized knot groups can be thought of as extensions of the classical knot group. For the square knot SK and the granny knot GK, we have an isomorphism G...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2002
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(02)00035-4