Tunnel numbers of small knots do not go down under connected sum

被引：10
|
作者：
Morimoto, K [1 ]
Schultens, J
机构：
[1] Takushoku Univ Tatemachi, Dept Math, Hachioji, Tokyo 193, Japan
[2] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 01期
关键词：
knots; connected sum; tunnel number;
D O I：
10.1090/S0002-9939-99-05160-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let K-1 and K-2 be two knots in S-3 and t(K-1), t(K-2) the tunnel numbers of them. In this paper, we show that if both K-1 and K-2 are small, then t(K-1#K-2) greater than or equal to t(K-1)+t(K-2). Moreover we show that t(K-1#K-2# ... #K-n) greater than or equal to t(K-1) + t(K-2) +...+t(K-n) for any small knots K-1, K-2,...,K-n.
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页码：269 / 278
页数：10
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