Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic and geometric aspects of rational $\Gamma$-inner functions   The set \[ \Gamma {\stackrel{\rm def}{=}} \{(z+w,zw):|z|\leq 1,|w|\leq 1\}
\subset {\mathbb{C}}^2 \] has intriguing complex-geometric properties; it has a
3-parameter group of automorphisms, its distinguished boundary is a ruled
surface homeomorphic to the M\"obius band and it has a special subvariety which
is the only complex geodesic that is invariant under all automorphisms. We
exploit this geometry to develop an explicit and detailed structure theory for
the rational maps from the unit disc to $\Gamma$ that map the boundary of the
disc to the distinguished boundary of $\Gamma$.

0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol