Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality functors for $n$-fold vector bundles   Double vector bundles may be dualized in two distinct ways and these duals
are themselves dual. These two dualizations generate a group, denoted
$\mathscr{D}\mathscr{F}_2$, which is the symmetric group $S_3$ on three
symbols. In the case of triple vector bundles the authors proved in a previous
paper that the corresponding group $\mathscr{D}\mathscr{F}_3$ is an extension
of $S_4$ by the Klein four-group. In this paper we show that the group
$\mathscr{D}\mathscr{F}_n$, for $n$-fold vector bundles, $n\geq 3$, is an
extension of $S_{n+1}$ by a certain product of groups of order 2, and show that
the centre is nontrivial if and only if $n$ is a multiple of 4. The methods
employ an interpretation of duality operations in terms of certain graphs on
$(n+1)$ vertices.

5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph