Heegaard Stability in Amalgamated 3-manifolds I: Connected Sums
نویسنده
چکیده
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 the irreducible case.
منابع مشابه
Additivity of Heegaard genera of bounded surface sums
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