Discrete derived categories II: the silting pairs CW complex and the stability manifold
Discrete derived categories II: the silting pairs CW complex and the stability manifold
复制标题
DOI：
10.1112/jlms/jdv069
复制
发表时间：
2014-07
期刊：
影响因子：
--
通讯作者：
Nathan Broomhead;David Pauksztello;D. Ploog
中科院分区：
文献类型：
--
作者：
Nathan Broomhead;David Pauksztello;D. Ploog
离散导出范畴最初由Vossieck [“The algebras with discrete derived categories”，J. Algebra 243（2001）168-176]研究，后来由Bobiobrski，Geiobrski and Skowroobrski [“Classification of discrete derived categories”，Cent. Eur. 2（2004）19-49]。在这篇文章中，我们定义了CW复形的淤泥对的三角范畴，并证明了它是可收缩的情况下，离散导范畴。我们提供了一个明确的嵌入从淤积CW复杂的稳定性流形。通过Qiu和Woolf的工作[“Contractible stability spaces and faithful braid group actions”，Preprint，2014，arXiv：1407.5986]，存在稳定流形到淤积对CW复形上的变形收缩。我们得到了离散导范畴的稳定性条件空间是可收缩的。
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.