The average edge order of triangulations of 3-manifolds with boundary
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- by Makoto Tamura PDF
- Trans. Amer. Math. Soc. 350 (1998), 2129-2140 Request permission
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.References
- Feng Luo and Richard Stong, Combinatorics of triangulations of $3$-manifolds, Trans. Amer. Math. Soc. 337 (1993), no. 2, 891–906. MR 1134759, DOI 10.1090/S0002-9947-1993-1134759-6
- C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744
- M. Tamura, The average edge order of triangulations of $3$-manifolds, Osaka J. Math. 33 (1996), 761–773.
- David W. Walkup, The lower bound conjecture for $3$- and $4$-manifolds, Acta Math. 125 (1970), 75–107. MR 275281, DOI 10.1007/BF02392331
Additional Information
- Received by editor(s): November 10, 1994
- Received by editor(s) in revised form: September 26, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 2129-2140
- MSC (1991): Primary 57Q15; Secondary 57M15
- DOI: https://doi.org/10.1090/S0002-9947-98-02014-5
- MathSciNet review: 1443199