Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz minimality of the multiplication maps of unit complex,
  quaternion and octonion numbers   We prove that the multiplication maps $\mathbb{s}^n \times \mathbb{s}^n
\rightarrow \mathbb{s}^n$ ($n = 1, 3, 7$) for unit complex, quaternion and
octonion numbers are, up to isometries of domain and range, the unique
Lipschitz constant minimizers in their homotopy classes. Other geometrically
natural maps, such as projections of Hopf fibrations, have already been shown
to be, up to isometries, the unique Lipschitz constant minimizers in their
homotopy classes, and it is suspected that this may hold true for all
Riemannian submersions of compact homogeneous spaces.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th