Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 273-300 |
Seitenumfang | 28 |
Fachzeitschrift | Journal of the London Mathematical Society |
Jahrgang | 93 |
Ausgabenummer | 2 |
Frühes Online-Datum | 28 Jan. 2016 |
Publikationsstatus | Veröffentlicht - 1 Apr. 2016 |
Abstract
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in: Journal of the London Mathematical Society, Jahrgang 93, Nr. 2, 01.04.2016, S. 273-300.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Discrete derived categories II
T2 - The silting pairs CW complex and the stability manifold
AU - Broomhead, Nathan
AU - Pauksztello, David
AU - Ploog, David
N1 - Funding information: The second author acknowledges the financial support of the EPSRC of the United Kingdom through the grant EP/K022490/1.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84971665332&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1407.5944
DO - 10.48550/arXiv.1407.5944
M3 - Article
AN - SCOPUS:84971665332
VL - 93
SP - 273
EP - 300
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 2
ER -