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Mathematische Annalen

, Volume 317, Issue 3, pp 489–508 | Cite as

On the super additivity of tunnel number of knots

  • Kanji Morimoto
Original article

Abstract. In the present paper, we show a necessary and sufficient condition for knots \(K_1, K_2\) in \(S^3\) (with some side condition) to have the super additivity of tunnel number under connected sum, i.e., \(t(K_1 \# K_2) = t(K_1) + t(K_2) + 1\).

Mathematics Subject Classification (1991): 57M25, 57N10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kanji Morimoto
    • 1
  1. 1.Department of Mathematics, Takushoku University, Tatemachi, Hachioji, Tokyo 193, Japan (e-mail : morimoto@la.takushoku-u.ac.jp) JP

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