Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the commutator of unit quaternions and the numbers 12 and 24   The quaternions are non-commutative. The deviation from commutativity is
encapsulated in the commutator of unit quaternions. It is known that the k-th
power of the commutator is null-homotopic if and only if k is divisible by 12.
The main purpose of this paper is to construct a concrete null-homotopy of the
12-th power of the commutator. Subsequently, we construct free S^3-actions on
S^7 x S^3 whose quotients are exotic 7-sphere and give a geometric explanation
for the order of the stable homotopy groups \pi_{n+3} (S^n). Intermediate
results of perhaps independent interest are a construction of the octonions
emphasizing the inclusion SU(3) \subset G_2, a detailed study of Duran's
geodesic boundary map construction, and explicit formulas for the
characteristic maps of the bundles G_2 \to S^6 and Spin(7) \to S^7.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex