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


Author: Henry Segerman
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 57Q15; Secondary 57M27
DOI: https://doi.org/10.1090/proc/13485
Published electronically: August 29, 2017
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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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Additional Information

Henry Segerman
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: segerman@math.okstate.edu

DOI: https://doi.org/10.1090/proc/13485
Received by editor(s): June 3, 2016
Received by editor(s) in revised form: September 18, 2016
Published electronically: August 29, 2017
Additional Notes: The author was supported in part by National Science Foundation grant DMS-1308767.
Communicated by: David Futer
Article copyright: © Copyright 2017 American Mathematical Society