Equivariant almost complex structures on quasitoric manifolds
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.
scientific article; zbMATH DE number 5655905