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 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 b1 < b.

Keywords
incompressible surface, Haken manifold.
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M25
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Publication
Received: 8 August 2000
Revised: 9 October 2000
Accepted: 9 October 2000
Published: 15 November 2000
Authors
Mario Eudave-Muñoz
Instituto de Matemáticas
UNAM
Ciudad Universitaria
04510 México DF
México
Jeremy Shor
250 E Houston St no 3J
New York City NY 10002
USA