Knot adjacency and satellites
نویسندگان
چکیده
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 کاملKnot Polynomials and Knot Homologies
This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories, and give some examples which illustrate a somewhat mysterious correspondence between them.
متن کاملKnot Energies and Knot Invariants
To record what has happened, ancient people tie knots. | I ching, the Chinese classic of 1027{771 B.C. Knots are fascinating objects. When fastening a rope, the distinction between a knot and a \slip-knot" (one that can be undone by pulling) must have been recognized very early in human history. We even developed a subconscious about knots: When we are puzzled or troubled, we have a feeling of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2004
ISSN: 0166-8641
DOI: 10.1016/j.topol.2003.08.001