Sweepouts of amalgamated 3-manifolds
arXiv:math/0507490 · doi:10.2140/agt.2006.6.171
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.
This is the version published by Algebraic & Geometric Topology on 24 February 2006
References in corpus (1)
Cited by in corpus (15)
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