Cohomology of torus manifold bundles
Jyoti Dasgupta, Bivas Khan, V. Uma

TL;DR
This paper provides algebraic descriptions of the cohomology and K-theory rings of torus manifold bundles, extending previous results to more general toric varieties and their associated bundles.
Contribution
It offers new presentations of cohomology and K-theory rings for torus manifold bundles, generalizing earlier work to include all smooth complete toric varieties.
Findings
Presented cohomology ring of E(X) over B
Described topological K-ring of E(X) over B
Extended results to general smooth complete toric varieties
Abstract
Let be a torus manifold with locally standard action of a compact torus of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds. Consider a principal bundle with total space and base with fibre and structure group . Let denote the total space of the associated torus manifold bundle. We give a presentation of the singular cohomology ring of E(X) as an algebra over the singular cohomology ring of and a presentation of the topological -ring of as an algebra over the topological -ring of . These are relative versions of the results of M. Masuda and T. Panov [13] on the cohomology ring of a torus manifold and P. Sankaran [14] on the topological -ring of a torus manifold. Further, they extend the results due to P. Sankaran and V. Uma [15] on the…
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory
