Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braids, conformal module and entropy   In the paper we discuss two invariants of conjugacy classes of braids. The
first invariant is the conformal module which occurred in connection with the
interest in the 13th Hilbert problem. The second is a popular dynamical
invariant, the entropy. It occurred in connection with Thurston's theory of
surface homeomorphisms. We prove that these invariants are related: They are
inverse proportional. This allows to use known results on entropy for
applications to the concept of conformal module. In particular, we give a short
conceptional proof of a theorem which appeared in connection with research on
the Thirteen's Hilbert Problem. We also give applications of the concept of
conformal module to the problem of isotopy of continuous objects involving
braids to the respective holomorphic objects. The objects considered here are
quasipolynomials of degree three as well as elliptic fiber bundles. A byproduct
of the proof is a systematic treatment of reducible braids and of the entropy
of mapping classes on Riemann surfaces of second kind, as well as expressions
of entropy and conformal module of conjugacy classes of reducible braids in
terms of the respective invariants of the irreducible components.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con