Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Combinatorics of triangulations of $ 3$-manifolds


Authors: Feng Luo and Richard Stong
Journal: Trans. Amer. Math. Soc. 337 (1993), 891-906
MSC: Primary 57Q15; Secondary 57M15
MathSciNet review: 1134759
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Abstract: In this paper, we study the average edge order of triangulations of closed $ 3$-manifolds and show in particular that the average edge order being less than $ 4.5$ implies that triangulation is on the $ 3$-sphere.


References [Enhancements On Off] (What's this?)

  • [Ba] David Barnette, The triangulations of the 3-sphere with up to 8 vertices, J. Combinatorial Theory Ser. A 14 (1973), 37–52. MR 0312511
  • [Gr] Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967. MR 0226496
  • [He] John Hempel, 3-Manifolds, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. Ann. of Math. Studies, No. 86. MR 0415619
  • [Od] Günter Ewald, Convex bodies and algebraic geometry, Discrete geometry and convexity (New York, 1982) Ann. New York Acad. Sci., vol. 440, New York Acad. Sci., New York, 1985, pp. 196–204. MR 809207, 10.1111/j.1749-6632.1985.tb14554.x
  • [Sp] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112

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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1134759-6
Article copyright: © Copyright 1993 American Mathematical Society