Pachner moves

In topology, a branch of mathematics, Pachner moves, named after Udo Pachner, are ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homeomorphic manifold. Pachner moves are also called bistellar flips. Any two triangulations of a piecewise linear manifold are related by a finite sequence of Pachner moves.
Definition.
Let formula_1 be the formula_2-simplex. formula_3 is a combinatorial "n"-sphere with its triangulation as the boundary of the "n+1"-simplex. 
Given a triangulated piecewise linear "n"-manifold formula_4, and a co-dimension "0" subcomplex formula_5 together with a simplicial isomorphism formula_6, the Pachner move on "N" associated to "C" is the triangulated manifold formula_7. By design, this manifold is PL-isomorphic to formula_4 but the isomorphism does not preserve the triangulation.