A generalization of Dehn-Sommerville relations to simple stratified spaces
type: Item
instance of: scholarly article
title: A generalization of Dehn-Sommerville relations to simple stratified spaces
zbMATH Open document ID: 0768.52008
DOI: 10.1007/BF02189306
published in: Discrete \& Computational Geometry
publication date: 1992-12-14T00:00:00Z
full work available at URL: https://eudml.org/doc/131233
review text: 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.
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 78492
zbMATH Keywords: polytopes
zbMATH Keywords: \(f\)-vectors
zbMATH Keywords: Dehn-Sommerville equations
zbMATH Keywords: smooth manifolds with boundaries
author: Ketan D. Mulmuley
reviewed by: Egon Schulte
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 78492