Surface Sum of Heegaard Splittings 
Received:March 16, 2007 Revised:May 26, 2007 
Key Words:
Heegaard splitting stabilized amalgamation.

Fund Project:the Specialized Research Fund for the Doctoral Program of Higher Education (No.200801411069). 

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Abstract: 
Suppose $M_i=V_i\cup W_i$~($i=1,2$) are Heegaard splittings. A homeomorphism $f:F_1\rightarrow F_2$ produces an attached manifold $M=M_1\cup_{F_1=F_2}M_2$, where $F_i \subset \partial_W_i$. In this paper we define a surface sum of Heegaard splittings induced from the Heegaard splittings of $M_1$ and $M_2$, and give a sufficient condition when the surface sum of Heegaard splitting is stabilized. We also give examples showing that the surface sum of Heegaard splittings can be unstabilized. This indicates that the surface sum of Heegaard splittings and the amalgamation of Heegaard splittings can give different Heegaard structures. 
Citation: 
DOI:10.3770/j.issn:1000341X.2009.03.022 
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