Tunnel number degeneration under the connected sum of prime knots
نویسندگان
چکیده
منابع مشابه
On the Growth Rate of Tunnel Number of Knots
Given a knot K in a closed orientable manifold M we define the growth rate of the tunnel number of K to be grt(K) = lim supn→∞ t(nK)−nt(K) n−1 . As our main result we prove that the Heegaard genus of M is strictly less than the Heegaard genus of the knot exterior if and only if the growth rate is less than 1. In particular this shows that a non-trivial knot in S is never asymptotically super ad...
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The tunnel number of a knot is an important invariant. It is defined to be the minimal number of disjoint properly embedded arcs in the knot’s exterior, such that drilling out these arcs creates a handlebody. Equivalently, it is the Heegaard genus of the knot exterior minus one. However, like many other interesting knot invariants, it is hard to compute in practice. The purpose of this paper is...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2013
ISSN: 0166-8641
DOI: 10.1016/j.topol.2013.03.010