Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infiniteness of $A_\infty$-types of gauge groups   Let $G$ be a compact connected Lie group and let $P$ be a principal
$G$-bundle over $K$. The gauge group of $P$ is the topological group of
automorphisms of $P$. For fixed $G$ and $K$, consider all principal $G$-bundles
$P$ over $K$. It is proved by Crabb--Sutherland and the second author that the
number of $A_n$-types of the gauge groups of $P$ is finite if $n<\infty$ and
$K$ is a finite complex. We show that the number of $A_\infty$-types of the
gauge groups of $P$ is infinite if $K$ is a sphere and there are infinitely
many $P$.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin