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A note on Kneser-Haken finiteness

Author(s): David Bachman
Journal: Proc. Amer. Math. Soc. 132 (2004), 899-902.
MSC (2000): Primary 57M99
Posted: July 9, 2003
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Abstract: Kneser-Haken finiteness asserts that for each compact 3-manifold $M$ there is an integer $c(M)$ such that any collection of $k>c(M)$ closed, essential, 2-sided surfaces in $M$ must contain parallel elements. We show here that if $M$ is closed, then twice the number of tetrahedra in a (pseudo)-triangulation of $M$ suffices for $c(M)$.

References:

[Hak61]
W. Haken.
Ein Verfahren zur Aufspaltung einer 3-Mannigfaltigkeit in irreduzible 3-Mannigfaltigkeiten.
Math. Zeit., 76:427-467, 1961. MR 25:4519c

[Hak68]
W. Haken.
Some Results on Surfaces in 3-Manifolds.
Math. Assoc. Amer., Prentice Hall, 1968. MR 36:7118

[Hat]
A. Hatcher.
Notes on basic 3-manifold topology.
Available at http://www.math.cornell. edu/$\sim$hatcher/.

[Hem76]
J. Hempel.
3-Manifolds, volume 86 of Annals of Mathematics Studies.
Princeton Univ. Press, Princeton, NJ, 1976. MR 54:3702

[JR]
W. Jaco and J. H. Rubinstein.
0-efficient triangulations of 3-manifolds.
To appear in the Journal of the AMS.

[Kne29]
H. Kneser.
Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten.
Jahresbericht der Deut. Math. Verein, 28:248-260, 1929.

[Neu]
W. Neumann.
Introduction to 3-manifolds (After A. Casson).
Lecture notes.

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Additional Information:

David Bachman
Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
Email: dbachman@calpoly.edu

DOI: 10.1090/S0002-9939-03-07049-7
PII: S 0002-9939(03)07049-7
Keywords: Incompressible surface, normal surface
Received by editor(s): September 7, 2002
Received by editor(s) in revised form: October 21, 2002
Posted: July 9, 2003
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2003, American Mathematical Society

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