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

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.

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

References

Forward citations

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

Volume 1, issue 1 (2001)

Mario Eudave-Muñoz and Jeremy Shor