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Henry Segerman : Connectivity of the set of triangulations of a 3- or 4-manifold

This is joint work with Hyam Rubinstein. Matveev and Piergallini independently show that the set of triangulations of a three-manifold is connected under 2-3 and 3-2 Pachner moves, excepting triangulations with only one tetrahedron. We give a more direct proof of their result which (in work in progress) allows us to extend the result to triangulations of four-manifolds.

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