Volume 1, issue 1 (2001)

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A universal bound for surfaces in 3-manifolds with a given Heegaard genus

Mario Eudave-Muñoz and Jeremy Shor

Algebraic & Geometric Topology 1 (2001) 31–37
 arXiv: math.GT/0008158
Abstract

It is shown that for given positive integers $g$ and $b$, there is a number $\mathsc{C}\left(g,b\right)$, such that any orientable compact irreducible 3-manifold of Heegaard genus $g$ has at most $\mathsc{C}\left(g,b\right)$ disjoint, nonparallel incompressible surfaces with first Betti number ${b}_{1}.

Keywords
incompressible surface, Haken manifold.
Primary: 57N10
Secondary: 57M25