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, and bistellar 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.
A note about bistellar operations on PL-manifolds with boundary / Casali, Maria Rita. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 56:(1995), pp. 257-262. [10.1007/BF01263566]
A note about bistellar operations on PL-manifolds with boundary
CASALI, Maria Rita
1995
Abstract
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, and bistellar 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.
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