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BOUNDING EDGE DEGREES IN TRIANGULATED 3-MANIFOLDS
 

Summary: BOUNDING EDGE DEGREES IN
TRIANGULATED 3-MANIFOLDS
NOEL BRADY1
, JON MCCAMMOND2
, AND JOHN MEIER
Abstract. In this note we prove that every closed orientable 3-manifold
has a triangulation in which each edge has degree 4, 5 or 6.
1. Introduction
All closed, orientable 3-manifolds can be constructed in a number of
seemingly simple and elegant ways. Examples include Heegaard diagrams,
branching over links in the 3-sphere, doing 0/1-Dehn 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
3-complex is the number of closed 3-cells 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 3-manifolds 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

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara
Brady, Noel - Department of Mathematics, University of Oklahoma

 

Collections: Mathematics