| A Lower Bound for the Heegaard Genera of Annulus Sum |
| Received:November 27, 2009 Revised:April 27, 2010 |
| Key Words:
genus distance annulus.
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| Fund Project:Supported by the Fundamental Research Funds for the Central Universities and the Key Grant of National Natural Science Foundation of China (Grant No.10931005). |
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| Abstract: |
| Let $M_{i}$, $i=1,2$, be a compact orientable 3-manifold, and $A_{i}$ an incompressible annulus on a component $F_i$ of $\partial M_i$. Suppose $A_{1}$ is separating on $F_{1}$ and $A_{2}$ is non-separating on $F_{2}$. Let $M$ be the annulus sum of $M_1$ and $M_2$ along $A_1$ and $A_2$. In the present paper, we give a lower bound for the genus of the annulus sum $M$ in the condition of the Heegaard distances of the submanifolds $M_1$ and $M_2$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.04.002 |
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