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Bounding edge degrees in triangulated $3$-manifolds

Author(s): Noel Brady; Jon McCammond; John Meier
Journal: Proc. Amer. Math. Soc. 132 (2004), 291-298.
MSC (2000): Primary 57Q15, 57M12
Posted: May 7, 2003
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Abstract: In this note we prove that every closed orientable $3$-manifold has a triangulation in which each edge has degree $4$, $5$ or $6$.

References:

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Daryl Cooper and William P. Thurston, Triangulating $3$-manifolds using $5$ vertex link types, Topology 27 (1988), no. 1, 23-25. MR 89d:57028

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Murray Elder, Jon McCammond, and John Meier, $3$-manifold triangulations and word-hyperbolicity, In preparation.

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Hugh M. Hilden, María Teresa Lozano, and José María Montesinos, On knots that are universal, Topology 24 (1985), no. 4, 499-504. MR 87a:57010

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John G. Ratcliffe, Foundations of hyperbolic manifolds, Springer-Verlag, New York, 1994. MR 95j:57011

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John Sullivan, New tetrahedrally close-packed structures, Preprint 2000.

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William P. Thurston, The geometry and topology of three-manifolds, Princeton lecture notes, 1978-80.

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Additional Information:

Noel Brady
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: nbrady@math.ou.edu

Jon McCammond
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: jon.mccammond@math.ucsb.edu

John Meier
Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
Email: meierj@lafayette.edu

DOI: 10.1090/S0002-9939-03-06981-8
PII: S 0002-9939(03)06981-8
Keywords: 3-manifold, triangulation, branched covering
Received by editor(s): January 14, 2002
Received by editor(s) in revised form: August 8, 2002
Posted: May 7, 2003
Additional Notes: The first author was partially supported under NSF grant no. DMS-9996342
The second author was partially supported under NSF grant no. DMS-9971682
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2003, American Mathematical Society

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