Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of locally homogeneous spaces   We study three different topologies on the moduli space $\mathscr{H}^{\rm
loc}_m$ of equivariant isometry classes of $m$-dimensional locally homogeneous
Riemannian spaces. As an application, we provide the first examples of locally
homogeneous spaces converging to a limit space in the pointed
$\mathcal{C}^{k,\alpha}$-topology, for some $k>1$, which do not admit any
convergent subsequence in the pointed $\mathcal{C}^{k+1}$-topology.

24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin