Classification of torus manifolds with codimension one extended actions
type: Item
instance of: scholarly article
title: Classification of torus manifolds with codimension one extended actions
zbMATH Open document ID: 1246.57082
author: Shintaro Kuroki
published in: Transformation Groups
publication date: 2011-11-30T00:00:00Z
full work available at URL: 111F0000020-09-5.pdf
review text: 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)].
reviewed by: Daniel Beltiţă
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 22F30
zbMATH DE Number: 5982609
zbMATH Keywords: toric manifold
zbMATH Keywords: compact Lie group
zbMATH Keywords: complex projective space
MaRDI profile type: Publication
OpenAlex ID: W2065112823
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DOI: 10.1007/S00031-011-9136-7
description: scientific article; zbMATH DE number 5982609