Stability conditions on $$\text {CY}_N$$ CY N categories associated to $$A_n$$ A n -quivers and period maps

We introduce the notion of ST‐pairs of triangulated subcategories, a prototypical example of which is the pair of the bound homotopy category and the bound derived category of a finite‐dimensional algebra. For an ST‐pair (C,D), we construct an injective order‐preserving map from silting objects in sans-serifC to bounded t‐structures on sans-serifD and show that the map is bijective if and only if sans-serifC is silting‐discrete if and only if sans-serifD is t‐discrete. Based on the work of Qiu and Woolf, the above result is applied to show that if sans-serifC is silting‐discrete then the stability space of sans-serifD is contractible. This is used to obtain the contractibility of the stability spaces of some Calabi–Yau triangulated categories associated to Dynkin quivers.

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“…Remark Corollary affirms [, Conjecture 1.3] and the second part of [, Conjecture 5.8] (see also [, Corollary 1.2; , Corollary 5.1]).…”

Section: Contractible Stability Spacessupporting

confidence: 72%

Discreteness of silting objects and t-structures in triangulated categories

Adachi

Mizuno

Yang

2018

Proc. London Math. Soc.

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“…More recently, an extension of the results of Bridgeland-Smith to certain polynomial quadratic differentials on C was carried out in [22,12]. There, CYn categories appear for n ≥ 2.…”

Section: Comparison With the Work Of Bridgeland-smithmentioning

confidence: 99%

Flat surfaces and stability structures

2017

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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 is achieved by new methods involving the complete classification of objects in these categories, which are defined in an elementary way. We also introduce a number of tools to deal with surfaces of infinite area, where structures similar to those in cluster algebra appear.

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“…Later [11], see also [43], showed that it was the universal cover in all these cases. When the underlying Dynkin diagram of Q is A n , [26] shows that Stab(Γ N Q) is the universal cover of the space of degree n+1 polynomials p n (z) with simple zeros. The central charges are constructed as periods of the quadratic differential p n (z) N −2 dz ⊗2 on P 1 , using the technique of [16].…”

Section: Introductionmentioning

confidence: 99%

Contractible stability spaces and faithful braid group actions

Qiu

Woolf

2018

Geom. Topol.

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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 category D (ΓN Q) associated to an ADE Dynkin quiver. In addition to showing that this is contractible we prove that the braid group Br (Q) acts freely upon it by spherical twists, in particular that the spherical twist group Br (ΓN Q) is isomorphic to Br (Q). This generalises Brav-Thomas' result for the N = 2 case. Other classes of triangulated categories with finite-type components in their stability spaces include locally-finite triangulated categories with finite rank Grothendieck group and discrete derived categories of finite global dimension.

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Stability conditions on $$\text {CY}_N$$ CY N categories associated to $$A_n$$ A n -quivers and period maps

Cited by 23 publications

References 22 publications

Discreteness of silting objects and t-structures in triangulated categories

Discreteness of silting objects and t-structures in triangulated categories

Flat surfaces and stability structures

Contractible stability spaces and faithful braid group actions

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