A universal bound for surfaces in 3-manifolds with a given Heegaard genus
arXiv:math/0008158 · doi:10.2140/agt.2001.1.31
Abstract
It is shown that for given positive integers g and b, there is a number C(g,b), such that any orientable compact irreducible 3-manifold of Heegaard genus g has at most C(g,b) disjoint, nonparallel incompressible surfaces with first Betti number b_1 < b.
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-2.abs.html