Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological invariants and Holomorphic Mappings   Invariants for Riemann surfaces covered by the disc and for hyperbolic
manifolds in general involving minimizing the measure of the image over the
homotopy and homology classes of closed curves and maps of the $k$-sphere into
the manifold are investigated. The invariants are monotonic under holomorphic
mappings and strictly monotonic under certain circumstances. Applications to
holomorphic maps of annular regions in $\mathbb{C}$ and tubular neighborhoods
of compact totally real submanifolds in general in $\mathbb{C}^n$, $n \geq 2$,
are given. The contractibility of a hyperbolic domain with contracting
holomorphic mapping is explained.

23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th