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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.
MORPHISMS BETWEEN INDECOMPOSABLE COMPLEXES IN THE BOUNDED DERIVED CATEGORY OF A GENTLE ALGEBRA
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