Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free curves and periodic points for torus homeomorphisms   We study the relationship between free curves and periodic points for torus
homeomorphisms in the homotopy class of the identity. By free curve we mean a
homotopically nontrivial simple closed curve that is disjoint from its image.
We prove that every rational point in the rotation set is realized by a
periodic point provided that there is no free curve and the rotation set has
empty interior. This gives a topological version of a theorem of Franks. Using
this result, and inspired by a theorem of Guillou, we prove a version of the
Poincar\'e-Birkhoff Theorem for torus homeomorphisms: in the absence of free
curves, either there is a fixed point or the rotation set has nonempty
interior.

37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int