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3-Manifold Containing Separating Incompressible Surfaces of All Positive Genera

3-Manifold Containing Separating Incompressible Surfaces of All Positive Genera
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摘要 In this paper, we shall prove that for any orientable 3-manifold M, there is a link L - K U K1 U K2 U K3 with four components in M, such that the complement of L, say ML, contains separating essential closed surfaces of all positive genera. In this paper, we shall prove that for any orientable 3-manifold M, there is a link L - K U K1 U K2 U K3 with four components in M, such that the complement of L, say ML, contains separating essential closed surfaces of all positive genera.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第6期1315-1318,共4页 数学学报(英文版)
基金 a grant (No.10171038) of NSFC
关键词 Incompressible surface KNOT 3-manifolds Incompressible surface, Knot, 3-manifolds
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参考文献6

  • 1Jaco, W.: Lectures on three-manifold Topology, Published by Amer. Math. Soc. Providence, Rhode Island, MR 81K, 57009 1980.
  • 2Qiu, R. F,: Incompressible surfaces in handlebodies and closed 3-manifolds of Heegaard genera two. PAMS,128, 3091-3097 (2000).
  • 3Jaco, W.: Surface embedded in M^2 × S^1. Canadian J. Math, XXII, 553-568 (1970).
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  • 5Kobayashi, T, Qiu, R. F, Wang, S. C, Rieck, Y.: Separating incompressible surfaces and stabilizations of Heegaard splittings. Proc. Camb. Phil. Soc, to appear.
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