ON (DISK, ANNULUS) PAIRS OF HEEGAARD SPLITTINGS THAT INTERSECT IN ONE POINT

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 1, 2009, pp.99-105
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.1.099

Title & Authors

ON (DISK, ANNULUS) PAIRS OF HEEGAARD SPLITTINGS THAT INTERSECT IN ONE POINT

Lee, Jung-Hoon;

Lee, Jung-Hoon;

Abstract

Let be a Heegaard splitting of a 3-manifold M, D be an essential disk in and A be an essential annulus in . Suppose D and A intersect in one point. First, we show that a Heegaard splitting admitting such a (D, A) pair satisfies the disjoint curve property, yet there are infinitely many examples of strongly irreducible Heegaard splittings with such (D, A) pairs. In the second half, we obtain another Heegaard splitting by removing the neighborhood of A from and attaching it to , and show that also has a (D, A) pair with .

Keywords

Heegaard splitting;essential annulus;disjoint curve property;

Language

English

References

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