Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves

Segerman, Henry

doi:10.1090/proc/13485

Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves
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Proc. Amer. Math. Soc. 145 (2017), 5391-5404 Request permission

Abstract:

Matveev and Piergallini independently showed that, with a small number of known exceptions, any triangulation of a three-manifold can be transformed into any other triangulation of the same three-manifold with the same number of vertices via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the Pachner graph of such triangulations is connected. In this paper, we extend this result to show that (again with a small number of known exceptions) the subgraph of the Pachner graph consisting of triangulations without degree one edges is also connected for single-vertex triangulations of closed manifolds and ideal triangulations of manifolds with non-spherical boundary components.

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