Amalgamations of Heegaard splittings in 3-manifolds without some essential surfaces
Amalgamations of Heegaard splittings in 3-manifolds without some essential surfaces
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DOI：
10.2140/agt.2009.9.2041
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发表时间：
2009-10
影响因子：
0.7
通讯作者：
Guoqiu Yang;Fengchun Lei
中科院分区：
文献类型：
--
作者：
Guoqiu Yang;Fengchun Lei
令M为紧凑的，可定向的 @ - 摩尔德3 – manifold，F为M的封闭基本表面，将M切入M1和M2，我们显示以下定理：假设。没有边界的表面/ G.F /。如果Mi具有距离vi的Heegaard分裂[Si Wi D.Si/ 2g.mi/ g.f/，i d 1;从新技术中，这是Schultens的引理的更强版本。
Let M be a compact, orientable, @–irreducible 3–manifold and F be a connected closed essential surface in M with g.F / 1 which cuts M into M1 and M2 . In the present paper, we show the following theorem: Suppose that there is no essential surface with boundary .Qi ; @Qi/ in .Mi ;F / satisfying .Qi/>2Cg.F / 2g.Mi/ , i D 1; 2 . Then g.M /Dg.M1/Cg.M2/ g.F / . As a consequence, we further show that if Mi has a Heegaard splitting Vi[Si Wi with distance D.Si/ 2g.Mi/ g.F / , i D 1; 2 , then g.M /D g.M1/Cg.M2/ g.F / . The main results follow from a new technique which is a stronger version of Schultens’ Lemma.