{
  "id": "1410.6468",
  "version": "v1",
  "published": "2014-10-23T19:44:17.000Z",
  "updated": "2014-10-23T19:44:17.000Z",
  "title": "Complexifications of infinite-dimensional manifolds and new constructions of infinite-dimensional Lie groups",
  "authors": [
    "Rafael Dahmen. Helge Glockner",
    "Alexander Schmeding"
  ],
  "comment": "32 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let M be a real analytic manifold modeled on a locally convex space and K be a non-empty compact subset of M. We show that if an open neighborhood of K in M admits a complexification which is a regular topological space, then the germ of the latter (as a complex manifold) is uniquely determined. If M is regular and the complexified modeling space of M is normal, then a regular complexification exists for some neighborhood of K. For each (real or complex) analytic regular manifold M modeled on a metrizable locally convex space and Banach-Lie group H, this allows the group Germ(K,H) of germs of H-valued analytic maps around K in M to be turned into an analytic Lie group which is regular in Milnor's sense. A special case is a regular real analytic Lie group structure on the group of real analytic H-valued maps on a compact real analytic manifold M (which, previously, had only been treated in the convenient setting of analysis). Combining our results concerning groups of germs with an idea by Neeb and Wagemann, one can also obtain a regular Lie group structure on the group of all real analytic H-valued mappings on the real line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-23T19:44:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite-dimensional lie groups",
      "infinite-dimensional manifolds",
      "real analytic manifold",
      "complexification",
      "locally convex space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6468D"
    }
  }
}