Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pullback invariants of Thurston maps   Associated to a Thurston map $f: S^2 \to S^2$ with postcritical set $P$ are
several different invariants obtained via pullback: a relation on the set of
free homotopy classes of curves in $S^2- P$, a linear operator on the free
$\R$-module generated by these homotopy classes of curves, a virtual
endomorphism on the pure mapping class group, an analytic self-map of an
associated Teichmueller space, and an analytic self-correspondence on an
associated moduli space. Viewing all of these objects as invariants of $f$, we
investigate harmonious relationships between their properties.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex