| Sufficient Conditions for Heegaard Splittings with Disjoint Curve Property |
| Received:November 28, 2006 Revised:September 14, 2007 |
| Key Words:
Heegaard splitting disjoint curve property.
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| Fund Project:the National Natural Science Foundation of China (No.10571034). |
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| Abstract: |
| In the paper, we give two conditions that the Heegaard splitting admits the disjoint curve property. The main result is that for a genus $g~(g\geq 2)$ strongly irreducible Heegaard splitting $(C_1,C_2;F)$, let $D_i$ be an essential disk in $C_i$, $i=1,2$, satisfying (1) at least one of $\partial D_1$ and $\partial D_2$ is separating in $F$ and $|\partial D_1 \cap \partial D_2 |\leq 2g-1$; or (2) both $\partial D_1$ and $\partial D_2 $ are non-separating in $F$ and $|\partial D_1 \cap \partial D_2 |\leq 2g-2 $, then $(C_1,C_2;F)$ has the disjoint curve property. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.02.026 |
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