2012/09/13 by Nathan Broomhead, Susana Pinheiro, Helena Reis +2 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Computer science #Engineering #Geology #Geomorphology #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Siltation #Stability (learning theory) #math.DS
paper · pdf · doi:10.1112/jlms/jdv069
arxiv created 2012/09/13 · openalex publication_date 2016/01/28 · arxiv updated 2017/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.