Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of torus manifold bundles   Let $X$ be a torus manifold with locally standard action of a compact torus
$T$ 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 $E$ and base $B$ with
fibre and structure group $T$. Let $E(X)$ 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 $B$
and a presentation of the topological $K$-ring of $E(X)$ as an algebra over the
topological $K$-ring of $B$. 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 $K$-ring of a torus manifold. Further, they
extend the results due to P. Sankaran and V. Uma [15] on the cohomology ring
and topological $K$-ring of toric bundles with fibre a smooth projective toric
variety, to a toric bundle with fibre any smooth complete toric variety.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con