紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2010, 47(1), p. 285-299

Characterization of homogeneous torus manifolds

Kuroki, Shintarô

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2010-03

This is the first of a series of papers which will be devoted to the study of the extended G-actions on torus manifolds (M^(2n), T^n), where G is a compact, connected Lie group whose maximal torus is T^n. The goal of this paper is to characterize codimension 0 extended G-actions up to essential isomorphism. For technical reasons, we do not assume that torus manifolds are omnioriented. The main result of this paper is as follows: a homogeneous torus manifold M^(2n) is (weak equivariantly) diffeomorphic to a product of complex projective spaces ΠℂP(l) and quotient spaces of a product of spheres ΠS^(2m)/A with standard torus actions, where A is a subgroup of Πℤ_2 generated by the antipodal involutions on S^(2m). In particular, if the homogeneous torus manifold M^(2n) is a compact (non-singular) toric variety or a quasitoric manifold, then M^(2n) is just a product of complex projective spaces ΠℂP(l).

10.18910/3559

3559

Characterization of homogeneous torus manifolds

Kuroki, Shintarô

Osaka University and Osaka City University, Departments of Mathematics

英語

2010-03

Osaka Journal of Mathematics

47

1

285

299

https://hdl.handle.net/11094/3559

10.18910/3559

https://doi.org/10.18910/3559