Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasitoric stably normally split manifolds   A smooth stably complex manifold is called a totally tangentially/normally
split manifold (TTS/TNS-manifold, for short, resp.) if the respective complex
tangential/normal vector bundle is stably isomorphic to a Whitney sum of
complex linear bundles, resp. In this paper we construct manifolds $M$ s.t. any
complex vector bundle over $M$ is stably equivalent to a Whitney sum of complex
linear bundles. A quasitoric manifold shares this property iff it is a
TNS-manifold. We establish a new criterion of the TNS-property for a quasitoric
manifold $M$ via non-semidefiniteness of certain higher-degree forms in the
respective cohomology ring of $M$. In the family of quasitoric manifolds, this
generalises the theorem of J. Lannes about the signature of a simply connected
stably complex TNS $4$-manifold. We apply our criterion to show the flag
property of the moment polytope for a nonsingular toric projective TNS-manifold
of complex dimension $3$.

15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics