Scharlemann, Martin; Schultens, Jennifer The tunnel number of the sum of \(n\) knots is at least \(n\). (English) Zbl 0929.57003 Topology 38, No. 2, 265-270 (1999). 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) Cited in 1 ReviewCited in 18 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) Keywords:Heegaard decomposition PDF BibTeX XML Cite \textit{M. Scharlemann} and \textit{J. Schultens}, Topology 38, No. 2, 265--270 (1999; Zbl 0929.57003) Full Text: DOI arXiv