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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. 相似文献
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Let M be a compact connected oriented 3-manifold with boundary, Q1, Q2 C 0M be two disjoint homeomorphic subsurfaces of cgM, and h : Q1 → Q2 be an orientation-reversing homeomorphism. Denote by Mh or MQ1=Q2 the 3-manifold obtained from M by gluing Q1 and Q2 together via h. Mh is called a self-amalgamation of M along Q1 and Q2. Suppose Q1 and Q2 lie on the same component F1 of δM1, and F1 - Q1 ∪ Q2 is connected. We give a lower bound to the Heegaard genus of M when M' has a Heegaard splitting with sufficiently high distance. 相似文献
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In this paper, we prove that a self-amalgamation of a strongly irreducible Heegaard splitting along disks is unstabilized. 相似文献
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