Cohomology of torus manifold bundles
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Abstract Let X be a 2n-dimensional torus manifold with a locally standard T ≅ (S1)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.
2016 ◽
Vol 27
(04)
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pp. 1650032
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2017 ◽
Vol 147
(5)
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pp. 971-992
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2007 ◽
Vol 09
(02)
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pp. 201-216
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2015 ◽
Vol 160
(2)
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pp. 353-377
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