Equivariant almost complex structures on quasitoric manifolds
type: Item
instance of: scholarly article
title: Equivariant almost complex structures on quasitoric manifolds
zbMATH Open document ID: 1195.57072
DOI: 10.1134/S0081543809030080
author: A. A. Kustarev
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2010-01-12T00:00:00Z
review text: A quasitoric manifold is a \(2n\)-dimensional compact smooth manifold \(M^{2n}\) with locally standard \(n\)-dimensional torus action whose orbit space is a simple polytope. \textit{M. W. Davis} and \textit{T. Januszkiewicz} [Duke Math. J. 62, No.~2, 417--451 (1991; Zbl 0733.52006)] posed the question of finding a criterion for the existence of an equivariant almost complex structure on a quasitoric manifold in terms of its characteristic function. The author solves this problem by proving the following main result of the paper. A quasitoric manifold \(M^{2n}\) admits a \(T^n\)-equivariant almost complex structure of and only if it has a positive omniorientation.
reviewed by: Jelena Grbić
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 52B70
zbMATH DE Number: 5655905
zbMATH Keywords: quasitoric manifold
zbMATH Keywords: equivariant almost complex structure
zbMATH Keywords: omniorientation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5655905