Classification of torus manifolds with codimension one extended actions
The paper under review provides the classification of \(2n\)-dimensional compact connected manifolds \(M\) acted on by the \(n\)-dimensional torus \(T^n\) with a nonempty fixed point set such that the corresponding action extends to an action of a compact Lie group \(G\) that contains \(T^n\) as maximal torus. The main result is that there exist seven isomorphism classes of such pairs \((M,G)\) and precise descriptions are provided for representatives of these isomorphism classes. As a corollary, one determines which ones of these manifolds are nonsingular toric varieties or quasitoric manifolds. The classification of the pairs \((M,G)\) under the additional hypotheses that \(M\) is oriented and the \(G\)-action is transitive was obtained in the author's earlier paper [Osaka J. Math. 47, No. 1, 285--299 (2010; Zbl 1238.57033)].
scientific article; zbMATH DE number 5982609
scientific article