Dehn surgeries that yield fibred 3-manifolds

被引：0
作者：
Yi Ni
机构：
[1] Columbia University,Department of Mathematics
[2] MIT,Department of Mathematics
来源：
Mathematische Annalen | 2009年 / 344卷
关键词：
Manifold; Boundary Component; Homology Class; Solid Torus; Floer Homology;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study Dehn surgeries on null-homotopic knots that yield fibred 3-manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai’s theory of sutured manifold decomposition. Such surgeries are negative examples to a question of Michel Boileau. Another result we will prove is about surgeries which reduce the Thurston norm of a fibred manifold.
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页码：863 / 876
页数：13
相关论文
共 18 条
  • [1] Boileau M.(1996)Non-zero degree maps and surface bundles over J. Differ. Geom. 43 789-806
  • [2] Wang S.(1983)Foliations and the topology of 3-manifolds J. Differ. Geom. 18 445-503
  • [3] Gabai D.(1987)Foliations and the topology of 3-manifolds II J. Differ. Geom. 26 461-478
  • [4] Gabai D.(1987)Foliations and the topology of 3-manifolds III J. Differ. Geom. 26 479-536
  • [5] Gabai D.(1989)Surgery on knots in solid tori Topology 28 1-6
  • [6] Gabai D.(2008)Knot Floer homology detects genus-one fibred knots Am. J. Math. 130 1151-1169
  • [7] Ghiggini P.(1989)Knots are determined by their complements J. Am. Math. Soc. 2 371-415
  • [8] Gordon C.(2004)Witten’s conjecture and property P Geom. Topol. 8 295-310
  • [9] Luecke J.(1997)Surfaces, surgery and unknotting operations Math. Ann. 308 615-632
  • [10] Kronheimer P.(1997)Dehn surgery on knots in 3-manifolds J. Am. Math. Soc. 10 835-864
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