Discrete derived categories II:the silting pairs CW complex and the stability manifold

Broomhead, Nathan and Pauksztello, David and Ploog, David (2016) Discrete derived categories II:the silting pairs CW complex and the stability manifold. Journal of the London Mathematical Society, 93 (2). pp. 273-300. ISSN 0024-6107

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Abstract

Discrete derived categories were studied initially by Vossieck [‘The algebras with discrete derived category’, J. Algebra 243 (2001) 168–176] and later by Bobiński, Geiß and Skowroński [‘Classification of discrete derived categories’, Cent. Eur. J. Math. 2 (2004) 19–49]. In this article, we define the CW complex of silting pairs for a triangulated category and show that it is contractible in the case of discrete derived categories. We provide an explicit embedding from the silting CW complex into the stability manifold. By work of Qiu and Woolf [‘Contractible stability spaces and faithful braid group actions’, Preprint, 2014, arXiv:1407.5986], there is a deformation retract of the stability manifold onto the silting pairs CW complex. We obtain that the space of stability conditions of discrete derived categories is contractible.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the London Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
87947
Deposited By:
Deposited On:
06 Oct 2017 19:35
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Apr 2020 05:40