A note about bistellar operations on PL-manifolds with boundary

In 1990, U. Pachner proved that simplicial triangulations of the same PL-manifold (with boundary) are always connected by a finite sequence of transformations belonging to two different groups:shelling operations (and their inverses), which work mostly with the boundary triangulations, andbistellar operations, which affect only the interior of the triangulations.The purpose of this note is to prove that, in case of simplicial triangulations coinciding on the boundary, bistellar operations are sufficient to solve the homeomorphism problem.Work performed under the auspicies of the GNSAGA of the CNR (National Research Council of Italy) and financially supported by MURST of Italy (project Geometria Reale e Complessa).