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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 $c(M)$.

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[JR]
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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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