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SILTING OBJECTS, SIMPLE-MINDED COLLECTIONS, t-STRUCTURES AND CO-t-STRUCTURES FOR FINITE-DIMENSIONAL ALGEBRAS
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Discrete derived categories II: The silting pairs CW complex and the stability manifold
"... Discrete derived categories were introduced by Vossieck [26] and classified by Bobiński, Geiß, Skrowoński [5]. 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. In particular, the sil ..."
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Discrete derived categories were introduced by Vossieck [26] and classified by Bobiński, Geiß, Skrowoński [5]. 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. In particular, the silting quiver of a discrete derived category is connected. We provide an explicit embedding from the silting CW complex into the stability manifold. By work of Woolf [28], 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.
