"The cd-index of bistellar flips"

DJ Wells
University of Kentucky

Monday, October 12, 2009
4:00 pm, 845 Patterson Office Tower

Abstract: Bistellar flips are certain local topological (or geometric, depending on the context) changes to a simplicial manifold. These operations have proven themselves useful in a number of areas of pure, experimental, and applied mathematics. One very nice feature of bistellar flips is that they change the g-vector (which encodes the number of faces in each dimension or "f-vector") in the simplest possible way -- by changing one component of the vector by 1. Since bistellar flips are local changes, they can be performed on PL-manifolds that are not necessarily simplicial. In such a case one may wish to keep track of the cd-index (which encodes the number of chains of faces of each type or "flag f-vector) instead of just the g-vector. I will derive two ways to calculate the change in the cd-index effected by a bistellar flip. One is in terms of a family of cd-polynomials introduced by Stanley (the simplicial shelling components of the cd-index). The other uses a recursion on these shelling components discovered by Ehrenborg and Readdy to give a recursion on the cd-index of bistellar flips.

This talk will include brief introductions to bistellar flips, the cd-index, and the simplicial shelling components.