Contractible stability spaces and faithful braid group actions

Qiu, Yu and Woolf, Jon (2018) Contractible stability spaces and faithful braid group actions. Geometry and Topology, 22 (6). pp. 3701-3760.

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Abstract

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 ( Γ N 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 ( Γ N Q ) is isomorphic to Br ( Q ) . This generalises the result of Brav–Thomas 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.

Item Type:	Article
Uncontrolled Keywords:	stability conditions, Calabi–Yau categories, spherical twists, braid groups
Depositing User:	Symplectic Admin
Date Deposited:	20 Mar 2018 10:13
Last Modified:	19 Jan 2023 06:38
DOI:	10.2140/gt.2018.22.3701
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3019204