Bounding edge degrees in triangulated 3-manifolds

Bounding edge degrees in triangulated $3$-manifolds
HTML articles powered by AMS MathViewer

by Noel Brady, Jon McCammond and John Meier PDF

Proc. Amer. Math. Soc. 132 (2004), 291-298 Request permission

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

D. Cooper and W. P. Thurston, Triangulating $3$-manifolds using $5$ vertex link types, Topology 27 (1988), no. 1, 23–25. MR 935525, DOI 10.1016/0040-9383(88)90004-3
Murray Elder, Jon McCammond, and John Meier, $3$-manifold triangulations and word-hyperbolicity, In preparation.
Hugh M. Hilden, María Teresa Lozano, and José María Montesinos, On knots that are universal, Topology 24 (1985), no. 4, 499–504. MR 816529, DOI 10.1016/0040-9383(85)90019-9
John G. Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathematics, vol. 149, Springer-Verlag, New York, 1994. MR 1299730, DOI 10.1007/978-1-4757-4013-4
John Sullivan, New tetrahedrally close-packed structures, Preprint 2000.
William P. Thurston, The geometry and topology of three-manifolds, Princeton lecture notes, 1978-80.