Corpus ID: 76658947

Topological structure of spaces of stability conditions and topological Fukaya type categories

  title={Topological structure of spaces of stability conditions and topological Fukaya type categories},
  author={Y. Qiu},
  journal={arXiv: Representation Theory},
  • Y. Qiu
  • Published 31 May 2018
  • Mathematics
  • arXiv: Representation Theory
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… Expand
2 Citations

Figures and Tables from this paper

Decorated Marked Surfaces: Calabi-Yau categories and related topics
This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration $\Delta$ on a marked surfaces $\mathbf{S}$, to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3Expand
$q$-Stability conditions via $q$-quadratic differentials for Calabi-Yau-$\mathbb{X}$ categories
We construct a quiver with superpotential $(Q_\mathbf{T},W_\mathbf{T})$ from a marked surface $\mathbf{S}$ with full formal arc system $\mathbf{T}$. Categorically, we show that the associatedExpand


Stability conditions on triangulated categories
This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas'sExpand
Flat surfaces and stability structures
We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured surfaces. This isExpand
Stability in Fukaya categories of surfaces
We construct stability conditions on Fukaya-type categories of surfaces from a large class of quadratic differentials. This is achieved by new methods involving the complete classification of objectsExpand
Stability conditions on CYN categories associated to An-quivers and period maps
In this paper, we study the space of stability conditions on a certain N- Calabi-Yau (CYN) category associated to an An-quiver. Recently, Bridgeland and Smith constructed stability conditions on someExpand
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the categoryExpand
Discrete derived categories II: the silting pairs CW complex and the stability manifold
This article defines the CW complex of silting pairs for a triangulated category and shows that it is contractible in the case of discrete derived categories and provides an explicit embedding from the silting CW complex into the stability manifold. Expand
Cotorsion pairs in the cluster category of a marked surface
We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. Under the one-to-one correspondence between the curves, valued closedExpand
Braid group actions on derived categories of coherent sheaves
This paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety $X$. The motivation for this is Kontsevich's homological mirror conjecture, togetherExpand
Contractible stability spaces and faithful braid group actions
We prove that any `finite-type' component of a stability space of a triangulated category is contractible. The motivating example of such a component is the stability space of the Calabi--Yau-$N$Expand
Calabi-Yau algebras
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of aExpand