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The tunnel number of the sum of $$n$$ knots is at least $$n$$. (English) Zbl 0929.57003
The tunnel number of a knot $$K$$ in $$S^3$$ is the minimum number of disjoint proper tunnels needed to be drilled into the complement of a tubular neighborhood of $$K$$ in order to obtain a handlebody. It has been known for some time now that if a knot has tunnel number $$1$$ then it is prime. This result is here generalized to show that if the tunnel number of $$K$$ is $$n$$ then $$K$$ can be expressed as a connected sum of $$\leq n$$ prime knots.
Reviewer: J.Levine (Waltham)

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)
##### Keywords:
Heegaard decomposition
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