Pachner's moves restricted


Hi,

Pachner moves enable you to transform any two triangulations of a
compact 3-manifold into one another, preserving the topological
structure along the way. Does anyone know of what happens if you
restrict your set of moves to only those that preserve or reduce the
number of vertices (even in the two dimensional case) ? What sort of
transformations are possible then?

I'd really appreciate if anyone could point me in any interesting
directions;

Thanks,

Stephen Lavelle

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