Logic Seminar

The talk explores connections between stellar moves on simplicial complexes (these are fundamental operations of combinatorial topology) and projective Fraïssé limits (this is a model theoretic construction with topological applications).

We identify a class of simplicial maps that arise from the stellar moves of welding and subdividing. We call these maps weld-division maps. Our main theorem asserts that the category of weld-division maps fulfills the projective amalgamation property. This gives an example of an amalgamation class that substantially differs from known classes. As a consequence, we give a combinatorial description of the geometric realization of a simplicial complex and an example of a combinatorially defined projective Fraïssé class whose canonical quotient space has topological dimension strictly bigger than 11.

The method of proof of the amalgamation theorem is new. It is not geometric or topological, but rather it consists of combinatorial calculations performed on finite sequences of finite sets. The set theoretic nature of the entries of the sequences is crucial to the arguments.