{
  "id": "1010.5269",
  "version": "v2",
  "published": "2010-10-25T21:16:05.000Z",
  "updated": "2010-11-01T20:50:03.000Z",
  "title": "The Mayer-Vietoris Property in Differential Cohomology",
  "authors": [
    "James Simons",
    "Dennis Sullivan"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AT",
    "math.DG",
    "math.QA"
  ],
  "abstract": "In [1] it was shown that K^, a certain differential cohomology functor associated to complex K-theory, satisfies the Mayer-Vietoris property when the underlying manifold is compact. It turns out that this result is quite general. The work that follows shows the M-V property to hold on compact manifolds for any differential cohomology functor J^ associated to any Z-graded cohomology functor J(, Z) which, in each degree, assigns to a point a finitely generated group. The approach is to show that the result follows from Diagram 1, the commutative diagram we take as a definition of differential cohomology, and Diagram 2, which combines the three Mayer-Vietoris sequences for J*(, Z), J*(, R) and J*(, R/Z).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-01T20:50:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mayer-vietoris property",
      "differential cohomology functor",
      "quite general",
      "complex k-theory",
      "z-graded cohomology functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5269S"
    }
  }
}