Algebraic & Geometric Topology

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

Mario Eudave-Munoz and Jeremy Shor

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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.

Article information

Algebr. Geom. Topol., Volume 1, Number 1 (2001), 31-37.

Received: 8 August 2000
Revised: 9 October 2000
Accepted: 9 October 2000
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

incompressible surface Haken manifold.


Eudave-Munoz, Mario; Shor, Jeremy. A universal bound for surfaces in 3-manifolds with a given Heegaard genus. Algebr. Geom. Topol. 1 (2001), no. 1, 31--37. doi:10.2140/agt.2001.1.31.

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