Heegaard Splittings of Sufficiently Complicated 3-manifolds Ii: Amalgamation
نویسنده
چکیده
Let M1 and M2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of ∂M1 to some component of ∂M2 by a homeomorphism φ. We show that when φ is “sufficiently complicated” then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of Mi 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 Mi, and possibly a Type II splitting of F × I, and (3) if there is no Type II splitting in such an expression then it is unique.
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Stabilizations of Heegaard Splittings of Sufficiently Complicated 3-manifolds (preliminary Report)
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