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论文类型：期刊论文

发表时间：2011-11-01

发表刊物：ACTA MATHEMATICA SINICA-ENGLISH SERIES

收录刊物：Scopus、SCIE、ISTIC

卷号：27

期号：11

页面范围：2229-2244

ISSN号：1439-8516

关键字：Tunnel number; Heegaard splitting; Heegaard distance; meridional surface

摘要：In this paper, we show the following result: Let K(i) be a knot in a closed orientable 3-manifold M(i) such that (M(i), K(i)) is not homeomorphic to (S(2) x S(1), x(0) x S(1)), i = 1,2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K(i)) is less than the difference of one and twice of the tunnel number of K(i). 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.
   We further show that if the distance of a Heegaard splitting of each knot complement is strictly bigger than twice the tunnel number of the knot (twice the sum of the tunnel number of the knot and one, respectively), then the tunnel number of connected sum of two such knots is additive (super additive, respectively).