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. 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 May 2021 03:10
DOI: 10.2140/gt.2018.22.3701
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3019204