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《Journal of Jilin University (Science Edition)》 1992-01
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On Non-Strongly Irreducible Heegaard Splittings

Lei Fengchun (Department of Mathematics,Jilin University,Changchun)  
For a Heegaard splitting (M,F) with genus n of an orientable closed 3-manifold M, we introduce the concept of disk index, δ(M,F), of (M,F), and infer that(1) (M,F) is not strongly irreducible iff δ(M,F)≥2;(2) (M,F) is reducible iff δ(M,F)≥max{2,n};(3) 2≤δ(M,F)n implies that M contains a 2-sided incompressible surface with positive genus.Thus we supply and improve the main work of Casson and Gordon in [3].
【Fund】: 国家自然科学基金
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