Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The minimal dimension of a sphere with an equivariant embedding of the
  bouquet of $g$ circles is $2g-1$   To embed the bouquet of $g$ circles $B_g$ into the $n$-sphere $S^n$ so that
its full symmetry group action extends to an orthogonal actions on $S^n$, the
minimal $n$ is $2g-1$. This answers a question raised by B. Zimmermann.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol