Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Teichm\"uller theory and collapse of flat manifolds   We provide an algebraic description of the Teichm\"uller space and moduli
space of flat metrics on a closed manifold or orbifold and study its boundary,
which consists of (isometry classes of) flat orbifolds to which the original
object may collapse. It is also shown that every closed flat orbifold can be
obtained by collapsing closed flat manifolds, and the collapsed limits of
closed flat 3-manifolds are classified.

7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics