Bruno Benedetti: Constructing manifolds from their simplices

A trick to understand manifolds better is to "assemble" them one piece at a time. For example, we could build a triangulated surface triangle after triangle, like in a jigsaw puzzle. Several ideas of this type have been explored so far, in quite different periods and fields of mathematics. For example, shellability came up in Schlaefli's studies on convex polytopes (1852). Collapsibility (by Whitehead, 1939) is a classical notion in combinatorial topology. Constructibility was first studied by Hochster, in a 1972 paper on Cohen-Macaulay rings. Finally, Local Constructibility was introduced in 1994 by two quantum physicists. We discuss the last notion, showing how it leads to a better understanding of the previous three. In particular, we obtain that in any fixed dimension, there are only exponentially many polytopes with N facets. This is joint work with Günter M. Ziegler.

Please observe the change of TIME and PLACE!