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- W1649582318 abstract "Let $M$ be a surface sum of 3-manifolds $M_1$ and $M_2$ along a bounded connected surface $F$ and $partial_i$ be the component of $partial M_i$ containing $F$. If $M_i$ has a high distance Heegaard splitting, then any minimal Heegaard splitting of $M$ is the amalgamation of those of $M^1, M^2$ and $M^*$, where $M^i=M_isetminuspartial_itimes I$, and $M^{*}=partial_1times Icup_{F} partial_2times I$. Furthermore, once both $partial_isetminus F$ are connected, then $g(M) = Minbigl{g(M_1)+g(M_2), alphabigr}$, where $alpha = g(M_1) + g(M_2) + 1/2(2chi(F) + 2 - chi(partial_1) - chi(partial_2)) - Maxbigl{g(partial_1), g(partial_2)bigl}$; in particular $g(M)=g(M_1)+g(M_2)$ if and only if $chi(F)geq 1/2Maxbigl{chi(partial_1), chi(partial_2)bigr}.$ The proofs rely on Scharlemann-Tomova's theorem." @default.
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- W1649582318 date "2008-06-18" @default.
- W1649582318 modified "2023-09-27" @default.
- W1649582318 title "Additivity of Heegaard genera of bounded surface sums" @default.
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