Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting a contraction of a simple curve traversed $m$ times   Suppose that $M$ is a $2$-dimensional oriented Riemannian manifold, and let
$\gamma$ be a simple closed curve on $M$. Let $m \gamma$ denote the curve
formed by tracing $\gamma$ $m$ times. We prove that if $m \gamma$ is
contractible through curves of length less than $L$, then $\gamma$ is
contractible through curves of length less than $L$. In the last section we
state several open questions about controlling length and the number of
self-intersections in homotopies of curves on Riemannian surfaces.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
3
The categories of this paper are: physics
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con