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...
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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...
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We establish results concerning the profinite completions of 3-manifold groups. In particular, we prove that the complement of the figure-eight knot SrK is distinguished from all other compact 3-manifolds by the set of finite quotients of its fundamental group. In addition, we show that if M is a compact 3-manifold with b1(M) = 1, and π1(M) has the same finite quotients as a free-by-cyclic grou...
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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...
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ion Based Information Technology is a way of understanding knowledge, interaction and control in many different domains. It explicitly covers humanities in this sense whereas the approaches mentioned above remained much more on a purely mathematical and/or computational side for better control and easier modeling. The concept “ABIT” (Abstraction Based Information Technology) proposed in (Calmet...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04358-4