대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권1호
  • /
  • Pages.99-105
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  • 2009
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON (DISK, ANNULUS) PAIRS OF HEEGAARD SPLITTINGS THAT INTERSECT IN ONE POINT

  • Lee, Jung-Hoon (SCHOOL OF MATHEMATICS KOREA INSTITUTE FOR ADVANCED STUDY)
  • 발행 : 2009.01.31
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초록

Let $M=H_1{\cup}_SH_2$ be a Heegaard splitting of a 3-manifold M, D be an essential disk in $H_1$ and A be an essential annulus in $H_2$. 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 $M=H'_1{\cup}_{S'}H'_2$ by removing the neighborhood of A from $H_2$ and attaching it to $H_1$, and show that $M=H'_1{\cup}_{S'}H'_2$ also has a (D, A) pair with $|D{\cap}A|=1$.

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참고문헌

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