Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensitive group actions on regular curves of almost $\leq n$ order   Let $X$ be a regular curve and $n$ be a positive integer such that for every
nonempty open set $U\subset X$, there is a nonempty connected open set
$V\subset U$ with the cardinality $|\partial_X(V)|\leq n$. We show that if $X$
admits a sensitive action of a group $G$, then $G$ contains a free subsemigroup
and the action has positive geometric entropy. As a corollary, $X$ admits no
sensitive nilpotent group action.

5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
1
The categories of this paper are: cs
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph