2014/07/22 by Nathan Broomhead, Broomhead, Nathan, David Pauksztello +3 · 1 citation
Mathematics · #05E10 #18E30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.CO #math.RT #msc:05E10 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1407.5944
27 pages, 3 figures; second version incorporates many improvements thanks to the anonymous referee; to be published in Journal of the LMS
arxiv created 2015/12/08 · arxiv updated 2015/12/09
Discrete derived categories were studied initially by Vossieck \citeVossieck and later by Bobiński, Geiß, Skowroński \citeBGS. 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, 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.