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AN ESTIMATE OF HEMPEL DISTANCE FOR BRIDGE SPHERES

Ayako Ido
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회보 (Bulletin of the KMS)|제52권 제3호|pp. 735-740

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참고문헌

키워드

distanceHeegaard splittingbridge decomposition
주제분류수학

초록

Tomova [8] gave an upper bound for the distance of a bridge surface for a knot with two different bridge positions in a 3-manifold. In this paper, we show that the result of Tomova [8, Theorem 10.3] can be improved in the case when there are two different bridge spheres for a link in S3.

Abstract

Tomova [8] gave an upper bound for the distance of a bridge surface for a knot with two different bridge positions in a 3-manifold. In this paper, we show that the result of Tomova [8, Theorem 10.3] can be improved in the case when there are two different bridge spheres for a link in S3.

참고문헌 (8)

  1. D. Bachman, "Distance and bridge position", Pacific J. Math, 219(2), pp.221~235 (2005)
  2. K. Hartshorn, "Heegaard splittings of Haken manifolds have bounded distance", Pacific J. Math, 204(1), pp.61~75 (2002)
  3. C. Hayashi, "Thin position of a pair (3-manifold, 1-submanifold)", Pacific J. Math, 197(2), pp.301~324 (2001)
  4. J. Hempel, "3-manifolds as viewed from the curve complex", Topology, 40(3), pp.631~657 (2001)
  5. Y. Jang, "Distance of bridge surfaces for links with essential meridional spheres", Pacific J. Math, 267(1), pp.121~130 (2014)
  6. J. Johnson, "Flipping bridge surfaces and bounds on the stable bridge number", Algebr. Geom. Topol, 11(4), pp.1987~2005 (2011)
  7. M. Scharlemann, "Alternate Heegaard genus bounds distance", Geom. Topol, 10, pp.593~617 (2006)
  8. M. Tomova, "Multiple bridge surfaces restrict knot distance", Algebr. Geom. Topol, 7, pp.957~1006 (2007)

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