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Some Sufficient Conditions for Tunnel Numbers of Connected Sum of Two Knots Not to Go Down

Some Sufficient Conditions for Tunnel Numbers of Connected Sum of Two Knots Not to Go Down
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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 （S^2 × S^1,x0 × S^1）, 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. 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）. 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 （S^2 × S^1,x0 × S^1）, 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. 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）.
作者 Guo Qiu YANG Feng Chun LEI
机构地区 School of Astronautics Department of Mathematics School of Mathematical Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第11期2229-2244,共16页 数学学报（英文版）
基金 The first author is supported by Development Program for Outstanding Young Teachers in Harbin Institute of Technology （HITQNJS.2009.029） the second author is supported by National Natural Science Foundation of China （Grant No. 15071034）
关键词 Tunnel number Heegaard splitting Heegaard distance meridional surface Tunnel number, Heegaard splitting, Heegaard distance, meridional surface
分类号 O511 [理学—低温物理] U45 [建筑科学—桥梁与隧道工程]
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参考文献25

  • 1Kobayashi, T.: A construction of arbitrarily high degeneration of tunnel number of knots under connected sum. J. Knot Theory Ramifications, 3, 179-186 (1994).
  • 2Morimoto, K.: There are knots whose tunnel number go down under connected sum. Proc. Amer. Ma~h. Soc., 123, 3527-3532 (1995).
  • 3Morimoto, K.: On the super additivity of tunnel number of knots. Math. Ann., 317, 489-508 (2000).
  • 4Morimoto, K.: The additivity of tunnel number knots. Topol. Appl., 53, 37-66 (1993).
  • 5Kobayashi, T., Rieck, Y.: Heegaard genus of the connected sum of m-small knots. Comm. Anal. Geom., 14, 1037-1077 (2006).
  • 6Morimoto3 K. Schultens, J.: Tunnel numbers of small knots do not go down under connected sum. Proc. Amer. Math. Soe., 128, 269-278 (2000).
  • 7Morimoto, K.: Tunnel number, connected sum and meridional essential surface. Topology, 39, 469-485 (2000).
  • 8Moriah, Y.: On boundary primitive manifolds and a theorem of Casson-Gordon. Topol. Appl., 125, 571-579 (2002).
  • 9Moriah, Y.: Heegaard splittings of knot exteriors. Geom. Topol. Mono., 12, 191-232 (2007).
  • 10Lustig, M., Moriah, Y.: Generalized Montesinos knots, tunnels and N-torision. Math. Ann., 295, 167-189 (1993).
Acta Mathematica Sinica,English Series
2011年 第11期

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