Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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AN ESTIMATE OF HEMPEL DISTANCE FOR BRIDGE SPHERES

  • Ido, Ayako (Department of Mathematics Education Aichi University of Education)
  • Received : 2013.03.06
  • Published : 2015.05.31
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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 $S^3$.

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References

  1. D. Bachman and S. Schleimer, Distance and bridge position, Pacific J. Math. 219 (2005), no. 2, 221-235. https://doi.org/10.2140/pjm.2005.219.221
  2. K. Hartshorn, Heegaard splittings of Haken manifolds have bounded distance, Pacific J. Math. 204 (2002), no. 1, 61-75. https://doi.org/10.2140/pjm.2002.204.61
  3. C. Hayashi and K. Shimokawa, Thin position of a pair (3-manifold, 1-submanifold), Pacific J. Math. 197 (2001), no. 2, 301-324. https://doi.org/10.2140/pjm.2001.197.301
  4. J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001), no. 3, 631-657. https://doi.org/10.1016/S0040-9383(00)00033-1
  5. Y. Jang, Distance of bridge surfaces for links with essential meridional spheres, Pacific J. Math. 267 (2014), no. 1, 121-130. https://doi.org/10.2140/pjm.2014.267.121
  6. J. Johnson and M. Tomova, Flipping bridge surfaces and bounds on the stable bridge number, Algebr. Geom. Topol. 11 (2011), no. 4, 1987-2005. https://doi.org/10.2140/agt.2011.11.1987
  7. M. Scharlemann andn M. Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006), 593-617. https://doi.org/10.2140/gt.2006.10.593
  8. M. Tomova, Multiple bridge surfaces restrict knot distance, Algebr. Geom. Topol. 7 (2007), 957-1006. https://doi.org/10.2140/agt.2007.7.957

Cited by

  1. Bridge splittings of links with distance exactly n vol.196, 2015, https://doi.org/10.1016/j.topol.2015.05.028