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COMMON STABILIZATIONS OF HEEGAARD SPLITTINGS OF KNOT EXTERIORS

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대한수학회 (The Korean Mathematical Society)|2010.01|대한수학회지 (Journal of the KMS)|제47권 제1호|pp. 113-122

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참고문헌

키워드

stabilizationHeegaard splittingunknotting tunnel
주제분류수학

초록

In [4], we gave a condition for a pair of unknotting tunnels of a non-trivial tunnel number one link to give a genus three Heegaard splitting of the link complement. In this paper we prove the corresponding result for tunnel number one knots.

Abstract

In [4], we gave a condition for a pair of unknotting tunnels of a non-trivial tunnel number one link to give a genus three Heegaard splitting of the link complement. In this paper we prove the corresponding result for tunnel number one knots.

참고문헌 (8)

  1. J. Hass, "Stabilization of Heegaard splittings", Geom. Topol., 13(4), pp.2029~2050 (2009)
  2. "Problems in low-dimensional topology"[URL]
  3. J. H. Lee, "Stabilizing Heegaard splittings of composite tunnel number two knots", J. Knot Theory Ramifications, 17(8), pp.1035~1041 (2008)
  4. J. H. Lee, "Common stabilizations of Heegaard splittings of link exteriors", Topology Appl., 150(1), pp.101~110 (2005)
  5. M. Scharlemann, "Heegaard splittings of (surface) × I are standard", Math. Ann., 295(3), pp.549~564 (1993)
  6. J. Schultens, "The stabilization problem for Heegaard splittings of Seifert fibered spaces", Topology Appl., 73(2), pp.133~139 (1996)
  7. E. Sedgwick, "An infinite collection of Heegaard splittings that are equivalent after one stabilization", Math. Ann., 308(1), pp.65~72 (1997)
  8. J. Singer, "Three-dimensional manifolds and their Heegaard diagrams", Trans. Amer. Math. Soc., 35(1), pp.88~111 (1933)

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