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Proceedings of the American Mathematical Society

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Thurston norm minimizing surfaces and skein trees for links in $ S\sp 3$

Author: Abigail Thompson
Journal: Proc. Amer. Math. Soc. 106 (1989), 1085-1090
MSC: Primary 57M25
MathSciNet review: 969321
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Abstract: This paper gives a method for constructing all links in $ {S^3}$, beginning with the unknot and adding at most one to the norm of the link at each stage. This has two corollaries. The first is that links with 'minimal' skein trees are fibered. The second is a complete list of all links with skein trees of height two.

References [Enhancements On Off] (What's this?)

  • [1] M. Scharlemann, Smooth spheres in $ {{\mathbf{R}}^4}$ with four critical points are standard, Invent. Math., 79 (1985), 125-141. MR 774532 (86e:57010)
  • [2] M. Scharlemann and A. Thompson, Link genus and the Conway moves, to appear in Comm. Math. Helv. MR 1022995 (91b:57006)
  • [3] J. Stallings, Constructions of fibered knots and links, A.M.S. Proc. Symp. Pure Math., 32 (1978), 55-60. MR 520522 (80e:57004)

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Article copyright: © Copyright 1989 American Mathematical Society

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