Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chiral vector bundles   This paper focuses on the study of a new category of vector bundles. The
objects of this category, called chiral vector bundles, are pairs given by a
complex vector bundle along with one of its automorphisms. We provide a
classification for the homotopy equivalence classes of these objects based on
the construction of a suitable classifying space. The computation of the
cohomology of the latter allows us to introduce a proper set of characteristic
cohomology classes: some of those just reproduce the ordinary Chern classes but
there are also new odd-dimensional classes which take care of the extra
topological information introduced by the chiral structure. Chiral vector
bundles provide a geometric model for topological quantum systems in class
AIII, namely for systems endowed with a (pseudo-)symmetry of chiral type. The
classification of the chiral vector bundles over sphere and tori (explicitly
computable up to dimension 4), recovers the commonly accepted classification
for topological insulator of class AIII which is usually based on the K-group
$K_1$. However, our classification turns out to be even richer since it takes
care also for possible non-trivial Chern classes.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph