Cohomology of torus manifold bundles

Rok, strany: 2019, 685 - 698

Let $X$ be a $2n$-dimensional torus manifold with a locally standard $T \cong ( S¹ )ⁿ$ 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 $p : E \rightarrow B$ and let $π : E(X) \rightarrow B$ 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 [masudapan] and [param] when the base $B=pt$. These also extend the results in [paramuma], obtained in the case of a smooth projective toric variety, to any smooth complete toric variety.

ISO 690:

Dasgupta, H., Khan, B., Uma, V. 2019. Cohomology of torus manifold bundles. In Mathematica Slovaca, vol. 69, no.3, pp. 685-698. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0257

APA:

Dasgupta, H., Khan, B., Uma, V. (2019). Cohomology of torus manifold bundles. Mathematica Slovaca, 69(3), 685-698. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0257