Free Products with Amalgamation and 3-manifolds
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چکیده
منابع مشابه
Heegaard Splittings of Sufficiently Complicated 3-manifolds Ii: Amalgamation
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 splitti...
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Let M1 and M2 be closed, irreducible 3-manifolds. Let Hi and Gi denote non-isotopic Heegaard surfaces in Mi, where Hi is unstabilized. Let H be the amalgamation of H1 and H2 and G be the amalgamation of G1 and G2 in M1#M2. Then H is not a stabilization of G. It follows that H and G are not isotopic, and that H is unstabilized. This answers a question of C. Gordon (Problem 3.91 from [Kir97]) in ...
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