{
  "id": "math/0212237",
  "version": "v3",
  "published": "2002-12-17T17:26:16.000Z",
  "updated": "2006-02-08T15:21:35.000Z",
  "title": "Stability conditions on triangulated categories",
  "authors": [
    "Tom Bridgeland"
  ],
  "comment": "A minor change in terminology (centered slope function becomes stability function). The result on stability conditions on curves of positive genus is removed since E. Macri found a much better proof in math/0411613. A false statement pointed out by S. Okada has also been removed. To appear in Annals of Maths",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "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 $\\Pi$-stability. From a mathematical point of view, the most interesting feature of the definition is that the set of stability conditions $\\Stab(\\T)$ on a fixed category $\\T$ 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 $\\Stab(\\T)$ with its natural topology is a manifold, possibly infinite-dimensional.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-02-08T15:21:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stability condition",
      "triangulated category",
      "natural topology",
      "dirichlet branes",
      "deformation result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12237B"
    }
  }
}