The Unstabilized Amalgamation of Heegaard Splittings along Disconnected Surfaces
Received:March 06, 2012  Revised:May 22, 2012
Key Word: unstabilized   distance   amalgamation   Heeaggard splitting.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10901029).
Author NameAffiliation
Xutao GAO School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Qilong GUO School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      Let $M$ be a 3-manifold, $\mathcal{F}$$= \{F_{1},F_{2},\ldots,F_{n}\}$ be a collection of essential closed surfaces in $M$ (for any $i,j\in \{1,...,n\}$, if $i\neq j$, $F_{i}$ is not parallel to $F_{j}$ and $F_i\cap F_j=\emptyset$) and $\partial_{0}M$ be a collection of components of $\partial M$. Suppose $M- \bigcup_{F_{i} \in \mathcal{F}} F_{i}\times (-1,1)$ contains $k$ components $M_{1},M_{2},\ldots,M_{k}$. If each $M_{i}$ has a Heegaard splitting $V_{i} \bigcup_{S_{i}} W_{i}$ with $d(S_{i}) > 4(g(M_{1})+ \cdots +g(M_{k}))$, then any minimal Heegaard splitting of M relative to $\partial_{0}M$ is obtained by doing amalgamations and self-amalgamations from minimal Heegaard splittings or $\partial$-stabilization of minimal Heegaard splittings of $M_{1},M_{2}, \ldots, M_{k}$.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.04.010
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