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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The average edge order of triangulations
of 3-manifolds with boundary


Author: Makoto Tamura
Journal: Trans. Amer. Math. Soc. 350 (1998), 2129-2140
MSC (1991): Primary 57Q15; Secondary 57M15
MathSciNet review: 1443199
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Abstract: Feng Luo and Richard Stong introduced the average edge order $\mu _0(K)$ of a triangulation $K$ and showed in particular that for closed 3-manifolds $\mu _0(K)$ being less than 4.5 implies that $K$ is on $S^3$. In this paper, we establish similar results for 3-manifolds with non-empty boundary; in particular it is shown that $\mu _0(K)$ being less than 4 implies that $K$ is on the 3-ball.


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DOI: http://dx.doi.org/10.1090/S0002-9947-98-02014-5
PII: S 0002-9947(98)02014-5
Received by editor(s): November 10, 1994
Received by editor(s) in revised form: September 26, 1996
Article copyright: © Copyright 1998 American Mathematical Society