Let M be a 3-manifold, F= ／{F1,F2,／…,Fn} be a collection of essential closed surfaces in M （for any i,j ∈ {1,...,n}, if i≠j, Fi is not parallel to Fj and Fi∩ Fj=Ф） and 0M be a collection of components of ...Let M be a 3-manifold, F= ／{F1,F2,／…,Fn} be a collection of essential closed surfaces in M （for any i,j ∈ {1,...,n}, if i≠j, Fi is not parallel to Fj and Fi∩ Fj=Ф） and 0M be a collection of components of M. Suppose M- ∪Fi∈F Fi×（-1,1） contains k components M1,M2…,Mk. If each Mi has a Heegaard splitting Vi ∪Si Wi with d（Si） 〉 4（g（M1）＋ … ＋g（Mk））, then any minimal Heegaard splitting of M relative to 0M is obtained by doing amalgamations and self-amalgamations from minimal Heegaard splittings or -stabilization of minimal Heegaard splittings of M1,M2…,Mk.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.10901029)
文摘Let M be a 3-manifold, F= ／{F1,F2,／…,Fn} be a collection of essential closed surfaces in M （for any i,j ∈ {1,...,n}, if i≠j, Fi is not parallel to Fj and Fi∩ Fj=Ф） and 0M be a collection of components of M. Suppose M- ∪Fi∈F Fi×（-1,1） contains k components M1,M2…,Mk. If each Mi has a Heegaard splitting Vi ∪Si Wi with d（Si） 〉 4（g（M1）＋ … ＋g（Mk））, then any minimal Heegaard splitting of M relative to 0M is obtained by doing amalgamations and self-amalgamations from minimal Heegaard splittings or -stabilization of minimal Heegaard splittings of M1,M2…,Mk.
