Sweepouts of amalgamated 3-manifolds
Geometric Topology
2009-09-29 v2
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.
Cite
@article{arxiv.math/0507490,
title = {Sweepouts of amalgamated 3-manifolds},
author = {David Bachman and Saul Schleimer and Eric Sedgwick},
journal= {arXiv preprint arXiv:math/0507490},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 24 February 2006