Algebraic and Geometric Topology 1 (2001), paper no. 2, pages 31-37.

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

Mario Eudave-Muñoz and Jeremy Shor

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.

Keywords. Incompressible surface, Haken manifold.

AMS subject classification. Primary: 57N10. Secondary: 57M25.

DOI: 10.2140/agt.2001.1.31

E-print: arXiv:math.GT/0008158

Submitted: 8 August 2000. (Revised: 9 October 2000.) Published: 15 November 2000.

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Mario Eudave-Muñoz and Jeremy Shor
Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria
04510 Mexico D.F., MEXICO

250 E. Houston St. no. 3J, New York City, NY 10002, U.S.A.


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