A survey of
twisted face-pairing 3-manifolds
J. W. Cannon, W. J. Floyd, and W. R. Parry
September 14, 2002
Abstract
The twisted face-pairing construction gives an efficient way to generate
face-pairing descriptions for many interesting closed 3-manifolds. Our
work in this paper is directed toward the goal of determining which
closed, connected, orientable 3-manifolds can be generated from
this construction.
We succeed in proving
that all lens spaces, the Heisenberg manifold (Nil geometry),
$S^2 \times S^1$, and all connected
sums of twisted face-pairing manifolds are twisted face-pairing
manifolds. We show how to obtain most
closed, connected, orientable, Seifert-fibered manifolds
as twisted face-pairing manifolds. It still seems unlikely
that all closed, connected, orientable 3-manifolds can be so obtained.
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