充分复杂三维流形II的Heegaard分裂：归并
Heegaard splittings of sufficiently complicated 3-manifolds II: Amalgamation
摘要：
设M_1和M_2是紧致的可定向的3-流形，M是由\bdy M_1的某个分支F通过同胚同构F与\bdy M_2的某个分支粘合而成的流形。我们证明了当M是“充分复杂的”时，（1）M_i的低亏格、不稳定、边界不稳定的Heegaard分裂的合并是M的不稳定分裂，（2）M的每一个低亏格、不稳定的Heegaard分裂都可以表示为M_i的不稳定、边界不稳定分裂的合并，也可能表示为F \times I的II型分裂，以及（3）如果在这样的表达式中不存在II型分裂，则它是唯一的。
英文摘要：
Let M_1 and M_2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of \bdy M_1 to some component of \bdy M_2 by a homeomorphism ϕ. We show that when ϕis "sufficiently complicated" then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of M_i is an unstabilized splitting of M, (2) every low genus, unstabilized Heegaard splitting of M can be expressed as an amalgamation of unstabilized, boundary-unstabilized splittings of M_i, and possibly a Type II splitting of F \times I, and (3) if there is no Type II splitting in such an expression then it is unique.
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