Euler flag enumeration of Whitney stratified spaces

The flag vector contains all the face incidence data of a polytope, and in the poset setting, the chain enumerative data. It is a classical result that for face lattices of polytopes, and more generally, Eulerian graded posets, the flag vector can be written as a cd-index, a non-commutative polynomial which removes all the linear redundancies among the flag vector entries. This holds for regular CW complexes. We relax the regularity conditions to show the cd-index exists for manifolds whose boundary has a Whitney stratification. I will describe how the setting of Whitney stratifications expands the nature of questions in the area of flag enumeration and, time permitting, briefly indicate work concerning manifold arrangements. This is joint work with Richard Ehrenborg and Mark Goresky. No prior knowledge is assumed other than knowing how to count.