Sweepouts of amalgamated 3-manifolds

Details Sweepouts of amalgamated 3-manifolds Sweepouts of amalgamated 3-manifolds

2005-07-25

arxiv.org/abs/math/0507490v2

Algebr. Geom. Topol. 6 (2006) 171-194

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 24 February 2006

Scientific paper

10.2140/agt.2006.6.171

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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