两个压缩体融合为一个压缩体的充分必要条件*

本文给出了两个压缩体沿紧致连通曲面(带边曲面或闭曲面)融合仍是一个压缩体(有非空负边界)的充分必要条件,还给出了两个3维流形沿着边界上的紧致连通带边曲面融合中的融合曲面为边界不可压缩的一个特征描述,同时还证明了压缩体的每个Heegaard分解是标准的.     

弱可逆有限自动机的化合与分解

本文证明了任何素数元延迟1步WIFA可以分解出一个延迟元与一个无延迟WIFA。故而k个素数元延迟1步WIFA的化合可以分解为一个无延迟WIFA与k个延迟元。另外对于二元延迟τ步WIFA,上述分解可行的充要条件是其所有状态的延迟步数均为τ。     

Hilbert空间有限强不可约分解算子

本文在Ｈｉｌｂｅｒｔ空间引入了有限强不可约分解算子及其强不可约分解在相似意义下的唯一性的概念,初步讨论了有限强不可约分解算子的性质,证明了一些算子的强不可约分解在相似意义下是唯一的．     

Heegaard分解的重新分块

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＭｂｅａｃｏｍｐａｃｔ 3 ｍａｎｉｆｏｌｄ .ＩｆｔｈｅｒｅｉｓａｐｒｏｐｅｒｌｙｅｍｂｅｄｄｅｄｃｌｏｓｅｄｓｕｒｆａｃｅＳｉｎＭｗｈｉｃｈｓｅｐａｒａｔｅｓＭｉｎｔｏｔｗｏｃｏｍｐｒｅｓｓｉｏｎｂｏｄｉｅｓＨ1ａｎｄＨ2 ,ｔｈｅｎＭｃａｎｂｅｗｒｉｔｔｅｎａｓＭ =Ｈ1∪ＳＨ2 .ＴｈｉｓｓｔｒｕｃｔｕｒｅｏｎＭｉｓｃａｌｌｅｄａＨｅｅｇａａｒｄｓｐｌｉｔｔｉｎｇｏｆＭａｎｄＳｉｓａｓｐｌｉｔｔｉｎｇｓｕｒｆａｃｅ .Ｈ1∪ＳＨ2 ｉｓｓａｉｄｔｏｂｅｒｅｄｕｃｉｂｌｅ…     

粗糙有限状态机的分解

利用代数的方法研究了粗糙有限状态机的可恢复性、连通性与可分离性等代数性质,得到了一个粗糙有限状态机是可恢复的当且仅当它的每一个准素粗糙子有限状态机都是强连通的当且仅当其每一个单生成粗糙子有限状态机都是准素的当且仅当其每一个非空连通粗糙子有限状态机都是准素的,给出了粗糙有限状态机不是连通的的充分必要条件,讨论了粗糙有限状态机的一些分解性质。     

具有三角分解可解李代数的表示

本文研究具有三角分解可解李代数和它的表示,探讨了具有三角分解可解李代数是广义限制李代数 的条件,对于某些 Ｓ ∈ Ｍａｐ（Ｂ,Ｆ）,在ｕ　ｓ（Ｌ,Ｓ）－模的范畴里,确定了不可约模和主不可分解模,并 对ｕ　ｓ（Ｌ,Ｓ）的块进行了描述．     

Topologically minimal surfaces versus self-amalgamated Heegaard surfaces

Let V ∪SW be a Heegaard splitting of M,such that αM = α-W = F1 ∪ F2 and g(S) = 2g(F1)= 2g(F2). Let V * ∪S*W * be the self-amalgamation of V ∪SW. We show if d(S) 3 then S* is not a topologically minimal surface.     

A proof of the Gordon Conjecture

A combinatorial proof of the Gordon Conjecture: The sum of two Heegaard splittings is stabilized if and only if one of the two summands is stabilized.     

Big Heegaard distance implies finite mapping class group

We show that if M is a closed three manifold with a Heegaard splitting with sufficiently big Heegaard distance then the subgroup of the mapping class group of the Heegaard surface, whose elements extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of M is finite.     

Reducing a Representation of Homotopy 3-spheres

In the present note we show that a representation of homotopy 3-spheres can be somewhat simplified under some circumstances.     

Spanning Annuli in 3—manifolds

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…     

Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

In this paper, we show the following result: Let K _i be a knot in a closed orientable 3-manifold M _i such that (M _i ,K _i ) is not homeomorphic to (S ₂ ×S ₁, x ₀ ×S ₁), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K _i ) is less than the difference of one and twice of the tunnel number of K _i . Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.