Regina Calculation Engine
Pachner moves on triangulations

A Pachner move on a triangulated n-manifold N works as follows:

We call the k-face the attaching face; this is the input to the Pachner move. The corresponding (n-k)-face in the new triangulation is called the belt face (in analogy with surgery).

Since the star of a k-face in the boundary of an (n+1)-simplex has (n+1-k) top-dimensional simplices, the star of the belt (n-k)-face has (k+1) top-dimensional simplices. The Pachner move therefore swaps (n+1-k) top-dimensional simplices for (k+1).


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For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).