A generalization of Dehn-Sommerville relations to simple stratified spaces (Q1196365)

The numbers \(f^ i(P)\) of \(i\)-dimensional faces of a simple convex \(d\)- polytope \(P\) satisfy a set of linear equations known as the Dehn- Sommerville equations. The author proves similar such equations for ``simple'' compact stratified spaces \(Z\), with \(f^ i(P)\) replaced by the sum \(f^ i(Z)=\sum_ S\chi(S)\) where \(S\) ranges over all \(i\)- dimensional strata of \(Z\) and \(\chi(S)\) denotes the Euler characteristic of \(S\). Examples of such spaces \(Z\) are the compact transverse intersections of arbitrary smooth manifolds with boundaries.