Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

被引：0
作者：
Guo Qiu Yang
Feng Chun Lei
机构：
[1] Harbin Institute of Technology,School of Astronautics
[2] Harbin Institute of Technology,Department of Mathematics
[3] Dalian University of Technology,School of Mathematical Sciences
来源：
Acta Mathematica Sinica, English Series | 2011年 / 27卷
关键词：
Tunnel number; Heegaard splitting; Heegaard distance; meridional surface; 57M99;
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学科分类号：
摘要：
In this paper, we show the following result: Let Ki be a knot in a closed orientable 3-manifold Mi such that (Mi,Ki) is not homeomorphic to (S2 ×S1, x0 ×S1), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(Ki) is less than the difference of one and twice of the tunnel number of Ki. Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.
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页码：2229 / 2244
页数：15
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