The Unstabilized Amalgamation of Heegaard Splittings along Disconnected Surfaces

摘要

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}, ifi≠j, Fi is not parallel to Fj and Fi ∩Fj = φ） and0 M be a collection of components of M. Suppose M-UFi ∈FFi×（-1, 1） contains k components M1 , M2 , . . . , Mk . If each M i has a Heegaard splitting ViUSiWi 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 .