Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57Q15, 57M15

Retrieve articles in all journals with MSC: 57Q15, 57M15

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society