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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
2.
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
3.
We define fat train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in S3.  相似文献
4.
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.  相似文献
5.
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.  相似文献
6.
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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