Sweepouts of amalgamated 3-manifolds

David Bachman; Saul Schleimer; Eric Sedgwick

doi:10.2140/agt.2006.6.171

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Sweepouts of amalgamated 3-manifolds

David Bachman·Saul Schleimer·Eric Sedgwick

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Abstract

We show that if two 3-manifolds with toroidal boundary are glued via a `sufficiently complicated' map then every Heegaard splitting of the resulting 3-manifold is weakly reducible. Additionally, if Z is a manifold obtained by gluing X and Y, two connected small manifolds with incompressible boundary, along a closed surface F. Then the genus g(Z) of Z is greater than or equal to 1/2(g(X)+g(Y)-2g(F)). Both results follow from a new technique to simplify the intersection between an incompressible surface and a strongly irreducible Heegaard splitting.

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BibTeX RIS

David Bachman, Saul Schleimer, Eric Sedgwick. 2009-02-26. Sweepouts of amalgamated 3-manifolds. https://doi.org/10.2140/agt.2006.6.171

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