 
Summary: BOUNDING EDGE DEGREES IN
TRIANGULATED 3MANIFOLDS
NOEL BRADY1
, JON MCCAMMOND2
, AND JOHN MEIER
Abstract. In this note we prove that every closed orientable 3manifold
has a triangulation in which each edge has degree 4, 5 or 6.
1. Introduction
All closed, orientable 3manifolds can be constructed in a number of
seemingly simple and elegant ways. Examples include Heegaard diagrams,
branching over links in the 3sphere, doing 0/1Dehn fillings on a cover of
the figure 8 knot complement [3], or gluing cubes together so that each edge
has degree 3, 4, or 5 (see [1]). Recall that the degree of an edge e in a
3complex is the number of closed 3cells which contain e. In this article we
add a new construction to this list: gluing tetrahedra together so that each
edge has degree 4, 5, or 6. Our primary motivation for this research comes
from recent work on triangulated 3manifolds with restricted edge degrees.
See [2] and [5].
As in the construction of Cooper and Thurston, our construction relies
heavily on the universality of the figure 8 knot complement. Specifically, we
