The number of small covers over cubes and the product of at most three simplices up to equivariant cobordism
type: Item
instance of: scholarly article
title: The number of small covers over cubes and the product of at most three simplices up to equivariant cobordism
zbMATH Open document ID: 1231.57028
author: Yanchang Chen
author: Yanying Wang
published in: Proceedings of the Japan Academy. Series A
publication date: 2011-10-12T00:00:00Z
review text: This paper considers the number of equivariant cobordism classes of small covers over the product of simplices. We recall that a small cover, defined by \textit{M. W. Davis} and \textit{T. Januszkiewicz} in [Duke Math. J. 62, No.2, 417--451 (1991; Zbl 0733.52006)], is a smooth closed manifold \(M^n\) with a locally standard \((\mathbb{Z}_2)^n\)-action such that its orbit space is a simple convex polytope. Denoting by \(\mathcal{M}_n\) the set of equivariant unoriented cobordism classes of all \(n\)-dimensional small covers, let \(\mathcal{M}_* = \sum_{n\geq 1}\mathcal{M}_n\), which is generated by the classes of small covers over the product of simplices. Since the equivariant cobordism class of a small cover over a simple convex polytope is determined by its tangential representation set, which can be identified with the characteristic function of the simple convex polytope, the authors using this function determine relevant results in what concerns the number of small covers over cubes and the product of at most three simplices up to equivariant cobordism.
reviewed by: Alice K. M. Libardi
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57R91
zbMATH DE Number: 5957831
zbMATH Keywords: equivariant cobordism
zbMATH Keywords: small cover
zbMATH Keywords: tangential representation
MaRDI profile type: Publication
full work available at URL: pjaa.87.95
OpenAlex ID: W2059039569
cites work: Small covers over prisms
cites work: The number of small covers over cubes
cites work: The number of orientable small covers over cubes
cites work: Convex polytopes, Coxeter orbifolds and torus actions
cites work: 2-torus manifolds, cobordism and small covers
cites work: Equivariant bordism and \((Z_ 2)^ k\) actions
DOI: 10.3792/PJAA.87.95
description: scientific article; zbMATH DE number 5957831