ON THE DEGENERATION OF TUNNEL NUMBERS UNDER A CONNECTED SUM

被引：6
作者：
Li, Tao [1 ]
Qiu, Ruifeng [2 ]
机构：
[1] Boston Coll, Dept Math, Chestnut Hill, MA 02467 USA
[2] E China Normal Univ, PMMP, Shanghai Key Lab, Dept Math, Shanghai 200241, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 04期
基金：
美国国家科学基金会;
关键词：
HEEGAARD-SPLITTINGS; CURVE COMPLEX; KNOTS; DISTANCE; GENUS; 3-MANIFOLDS; ADDITIVITY; SURFACES; PRIME;
D O I：
10.1090/tran/6473
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that, for any integer n >= 3, there is a prime knot k such that (1) k is not meridionally primitive, and (2) for every m- bridge knot k' with m <= n, the tunnel numbers satisfy t(k#k') <= t(k). This gives counterexamples to a conjecture of Morimoto and Moriah on tunnel numbers under a connected sum and meridionally primitive knots.
引用
收藏
页码：2793 / 2807
页数：15
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