Affiliation:
1. Department of Mathematics Indian , Institute of Technology-Madras , Chennai , India
Abstract
Abstract
Let X be a 2n-dimensional torus manifold with a locally standard T ≅ (S
1)
n
action whose orbit space is a homology polytope. Smooth complete complex toric varieties and quasitoric manifolds are examples of torus manifolds. Consider a principal T-bundle p : E → B and let π : E(X) → B be the associated torus manifold bundle. We give a presentation of the singular cohomology ring of E(X) as a H
*(B)-algebra and the topological K-ring of E(X) as a K
*(B)-algebra with generators and relations. These generalize the results in [17] and [19] when the base B = pt. These also extend the results in [20], obtained in the case of a smooth projective toric variety, to any smooth complete toric variety.
Reference24 articles.
1. Atiyah, M. F.—Hirzebruch, F.—Adams, J. F.—Shepherd, G. C.: Vector bundles and homogeneous spaces. London Math. Soc. Lecture Note Ser., Cambridge University Press, 1972, pp. 196–222.
2. Atiyah, M. F.—MacDonald, I. G.: Introduction to Commutative Algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
3. Baggio, S.: Equivariant K-theory of smooth toric varieties, Tohoku Math. J. (2) 59(2) (2007), 203–231.
4. Bredon, G. E.: Introduction to Compact Transformation Groups. Pure Appl. Math. 46, Academic Press, New York-London, 1972.
5. Buchstaber, V. M.—Panov, T. E.: Toric Topology. Math. Surveys Monogr. 204, AMS, Providence, RI, 2015.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献