The Pants Sum of High Distance Heegaard Splittings
Received:December 04, 2012  Revised:September 11, 2013
Key Words: pants sum   Heegaard distance   Heegaard genus.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11226084).
Author NameAffiliation
Shuxi WANG School of Mathematics, Liaoning Normal University, Liaoning 116029, P. R. China 
Nan NI School of Mathematics, Liaoning Normal University, Liaoning 116029, P. R. China 
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Abstract:
      Let $M_i$ be a compact orientable 3-manifold, and $F_i$ be an incompressible surface on $\partial M_i$, $i=1,2$. Let $f: F_1\rightarrow F_2$ be a homeomorphism, and $M=M_{1}\cup_{f} M_{2}$. In this paper, under certain assumptions for the attaching surface $F_i$, we show that if both $M_1$ and $M_2$ have Heegaard splittings with distance at least $2(g(M_1)+g(M_2))+1$, then $g(M)=g(M_1)+g(M_2)$.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.02.011
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