Complexity of triangulations of the projective space

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It is known that any two triangulations of a compact 3-manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two triangulations of the 3-dimensional projective space, in terms of the number of tetrahedra.
10 pages, 3 figures. Revised version, to appear in Top. Appl

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