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A note on Kneser-Haken finiteness


Author: David Bachman
Journal: Proc. Amer. Math. Soc. 132 (2004), 899-902
MSC (2000): Primary 57M99
DOI: https://doi.org/10.1090/S0002-9939-03-07049-7
Published electronically: July 9, 2003
MathSciNet review: 2019971
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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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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-03-07049-7
Keywords: Incompressible surface, normal surface
Received by editor(s): September 7, 2002
Received by editor(s) in revised form: October 21, 2002
Published electronically: July 9, 2003
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2003 American Mathematical Society