{
  "id": "math/0603383",
  "version": "v2",
  "published": "2006-03-15T19:41:09.000Z",
  "updated": "2006-11-14T16:11:22.000Z",
  "title": "Nested set complexes of Dowling lattices and complexes of Dowling trees",
  "authors": [
    "Emanuele Delucchi"
  ],
  "comment": "14 pages, 2 figures, corrected typos, added references",
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice Q(G) and of its subposet of the G-symmetric partitions Q_G which was recently introduced by Hultman together with the complex of G-symmetric phylogenetic trees T_G. Hultman shows that T_G and Q_G are homotopy equivalent and Cohen-Macaulay, and determines the rank of their top homology. An application of the theory of building sets and nested set complexes by Feichtner and Kozlov shows that in fact T_G is subdivided by the order complex of Q_G. We introduce the complex of Dowling trees T(G) and prove that it is subdivided by the order complex of Q(G) and contains T_G as a subcomplex. We show that T(G) is obtained from T_G by successive coning over certain subcomplexes. We explicitly and independently calculate how many homology spheres are added in passing from T_G to T(G).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-14T16:11:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20"
    ],
    "keywords": [
      "nested set complexes",
      "dowling trees",
      "dowling lattice",
      "order complex",
      "g-symmetric phylogenetic trees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3383D"
    }
  }
}