Stability conditions on triangulated categories

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This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of Π-stability. From a mathematical point of view, the most interesting feature of the definition is that the set of stability conditions () on a fixed category has a natural topology, thus defining a new invariant of triangulated categories. After setting up the necessary definitions I prove a deformation result which shows that the space () with its natural topology is a manifold, possibly infinite-dimensional.