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Let Mi, i = 1,2, be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of OMi. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper, we give a lower bound for the genus of the annulus sum M in the condition of the Heegaard distances of the submanifolds M1 and M2 相似文献
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本文我们描述了使两个柄体带和有不可压缩边界的一个条件,作为应用,我们证明了同伦3-球面的一个表示在某种情形可以被简化。 相似文献
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设(M;H_1,H_2;F_0)为带边3-流形M的一个SD-分解.称该分解为可约的(或弱可约的)若存在本质圆片D_1■H)_1,D_2■H_2使得■D_1,■D_2■F_0并且■D_1=■D_2(或■D_1∩■D_2=■).称(M;H_1,H_2;F_0)为内亏格1若F_0为穿孔环面.本文主要结果:一个弱可约的内亏格1的SD-分解或是可约的或是双经的. 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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Al3-manifOldsandsurfacesconsideredinthisPaperareassumedtobecompactandori-entable,andallconcePtsandnotationsnotdefinedinthepaperareStandardfsee,forexample[2,3j.AcompressionbodyHisconstructedbyadding2-handlestoSXIalongacollectionofpairwisdisjointsimpleclosedcurvesonSX{o},andcaPpingoffanyresulting2-spherebound-arycomponentSwith3-balls,whereSisaconnectedclosedorientablesurface.ThecomponentSX{1}Of8Hisdenoted8 Handthesurface8H-8 H,whichmayormaynotbeconnect-ed,isdenoted8H.If8H=gi,Hisahandleb… 相似文献
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Werestrictourconsiderationtoorientableandcompactcategory .Fordefinitionsandterminology ,seeforexample ,[1 ]and [2 ]. LetSbeaclosedorientablesurfacewithpositivegenus .Inthispaper ,MalwaysdenotesS×I ,andS0 =S× 0 ,S1=S× 1 .AnannulusAinMwithitstwoboundarieslyinginS0andS1r… 相似文献
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Let S be a closed orientable surface of genus g ≥ 2,and C(S)the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C(S),which can be regarded as an analogue to the edge path between vertices in C(S).We show that C(S)is 2P-connected,and the 2-diameter of C(S)is infinite. 相似文献