Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological structure of spaces of stability conditions and topological
  Fukaya type categories   This is a survey on two closely related subjects. First, we review the study
of topological structure of `finite type' components of spaces of Bridgeland's
stability conditions on triangulated categories. The key is to understand
Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological
realizations of various Fukaya type categories, namely cluster/Calabi-Yau and
derived categories from surfaces. The corresponding spaces of stability
conditions are of `tame' nature and can be realized as moduli spaces of
quadratic differentials due to Bridgeland-Smith and
Haiden-Katzarkov-Kontsevich.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin