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2009 Amalgamations of Heegaard splittings in $3$–manifolds without some essential surfaces
Guoqiu Yang, Fengchun Lei
Algebr. Geom. Topol. 9(4): 2041-2054 (2009). DOI: 10.2140/agt.2009.9.2041

Abstract

Let M be a compact, orientable, –irreducible 3–manifold and F be a connected closed essential surface in M with g(F)1 which cuts M into M1 and M2. In the present paper, we show the following theorem: Suppose that there is no essential surface with boundary (Qi,Qi) in (Mi,F) satisfying χ(Qi)2+g(F)2g(Mi)+1, i=1,2. Then g(M)=g(M1)+g(M2)g(F). As a consequence, we further show that if Mi has a Heegaard splitting ViSiWi with distance D(Si)2g(Mi)g(F), i=1,2, then g(M)=g(M1)+g(M2)g(F).

The main results follow from a new technique which is a stronger version of Schultens’ Lemma.

Citation

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Guoqiu Yang. Fengchun Lei. "Amalgamations of Heegaard splittings in $3$–manifolds without some essential surfaces." Algebr. Geom. Topol. 9 (4) 2041 - 2054, 2009. https://doi.org/10.2140/agt.2009.9.2041

Information

Received: 28 May 2009; Revised: 3 September 2009; Accepted: 5 September 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1188.57016
MathSciNet: MR2551661
Digital Object Identifier: 10.2140/agt.2009.9.2041

Subjects:
Primary: 57M99, 57N10
Secondary: 57M27

Rights: Copyright © 2009 Mathematical Sciences Publishers

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