{
  "id": "0911.2749",
  "version": "v1",
  "published": "2009-11-14T07:36:43.000Z",
  "updated": "2009-11-14T07:36:43.000Z",
  "title": "The $S^1$-Equivariant Cohomology of Spaces of Long Exact Sequences",
  "authors": [
    "T. B. Williams"
  ],
  "categories": [
    "math.AT",
    "math.AC"
  ],
  "abstract": "Let $S$ denote the graded polynomial ring $\\C[x_1,...,x_m]$. We interpret a chain complex of free $S$-modules having finite length homology modules as an $S^1$-equivariant map $\\C^m\\sm\\{0\\} \\to X$, where $X$ is a moduli space of exact sequences. By computing the cohomology of such spaces $X$ we obtain obstructions to such maps, including a slight generalization of the Herzog-K\\\"uhl equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-14T07:36:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N91"
    ],
    "keywords": [
      "long exact sequences",
      "equivariant cohomology",
      "finite length homology modules",
      "slight generalization",
      "chain complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.2749W"
    }
  }
}