共查询到17条相似文献,搜索用时 78 毫秒
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设$M_i~(i=1,2)$是一个紧致可定向的三维流形, $F_i$是$M_i$边界上的一个不可压缩曲面, $M=M_{1}\cup_{f}M_{2}$, 其中$f$是$F_1$到$F_2$一个同胚,对于具有特定条件的相粘曲面$F_i$, 如果$M_i$具有一个Heegaard距离至少是$2(g(M_1)+g(M_2))+1$的Heegaard分解,则$g(M)=g(M_1)+g(M_2)$. 相似文献
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Let F= F(X) be a free group of rand n, A be a finite subset of F(X) and x∈X be a generator. The theorem states that x can be denoted as a rotation-inserting word of A if x is in the normal closure of A in F(X). Finally, an application of the theorem in Heegaard splitting of 3manifolds is given. 相似文献
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§ 1.Introduction LetMbeacompact 3 manifold .IfthereisaproperlyembeddedclosedsurfaceSinMwhichseparatesMintotwocompressionbodiesH1andH2 ,thenMcanbewrittenasM =H1∪SH2 .ThisstructureonMiscalledaHeegaardsplittingofMandSisasplittingsurface .H1∪SH2 issaidtobereducible… 相似文献
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Suppose Mi = Vi ∪ Wi (i = 1,2) are Heegaard splittings. A homeomorphism f : F1 → F2 produces an attached manifold M = M1 ∪F1=F2 M2, where Fi ∪→ δ_Wi. In this paper we define a surface sum of Heegaard splittings induced from the Heegaard splittings of M1 and M2, 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. 相似文献
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In the paper,we give two conditions that the Heegaard splitting admits the disjoint cnrve property.The main result is that for a genus g(g≥2)strongly irreducible Heegaard splitting(C1,C2;F),let Di be an essential disk in Ci,i=1,2,satisfying(1)at least one of (の)D4 and (の)D2 is separating in F and |(の)D1 (∩)(の)D2|≤ 2g-1;or(2)both (の)D1 and (の)D2 are non-separating in F and |(の)D1 (∩)(の)D2|≤ 2g-2,then(C1,C2;F)has the disjoint curve property. 相似文献
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Lei Fengchun Zhang Ying 《东北数学》1998,(4)
§1.BackgroundandMainResultsSincetheconceptofthinpositionforknotsinthe3-spherewasdevelopedbyGabai[1],manyitsapplicationstodeal... 相似文献
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设$V\cup_SW$是一个闭的三维流形亏格为$g$的, 弱可约的Heegaard分解, 并且在合痕意义下只有有限组位于曲面不同侧的不相交的压缩圆片, 则它存在一个广义的Heegaard分解: $V\cup_SW=(V_1\cup_{S_1}W_1)\cup_F(W_2\cup_{S_2}V_2)$, 并且满足对于每个$i=1,2$, 压缩体$W_i$都只有一个分离的压缩圆片且$d(S_i)\geq 2$. 进一步的, 如果有有限且多于1组不相交的压缩圆片, 则至少一个$d(S_i)$等于2, 并且Heegaard曲面满足临界性质. 相似文献
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§1.IntroductionTheconceptofreducibleHeegaardsplitingswasfirstdevelopedbyHaken[1].Itsrela-tiontothecorresponding3-manifoldscon... 相似文献
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Let Mi be a compact orientable 3-manifold, and Fi be an incompressible surface on δMi, i -= 1,2. Let f : F1 →F2 be a homeomorphism, and M = M1 UI M2. In this paper, under certain assumptions for the attaching surface Fi, we show that if both M1 and M2 have Heegaavd splittings with distance at least 2(g(M1)+ g(M2))+ 1, then g(M) = g(M1)+g(M2). 相似文献
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Zou YAN-QING LIU XI-MIN 《数学研究通讯:英文版》2014,(3):193-200
We prove that for any integer n≥2 and g ≥ 2, there are bounded 3-manifolds admitting distance n, genus g Heegaard splittings with any given bound-aries. 相似文献