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Tunnel numbers of small knots do not go down under connected sum |
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| Authors: | Kanji Morimoto Jennifer Schultens |
| Institution: | Department of Mathematics, Takushoku University Tatemachi, Hachioji, Tokyo 193, Japan ; Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322 |
| Abstract: | Let  and  be two knots in  and  ,  the tunnel numbers of them. In this paper, we show that if both  and  are small, then  . Moreover we show that  for any small knots  . |
| Keywords: | Knots connected sum tunnel number |
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