{
  "id": "1812.07335",
  "version": "v1",
  "published": "2018-12-18T12:52:22.000Z",
  "updated": "2018-12-18T12:52:22.000Z",
  "title": "Homomorphism Complexes and Maximal Chains in Graded Posets",
  "authors": [
    "Benjamin Braun",
    "Wesley K. Hough"
  ],
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special emphasis on finite products of chains. For the special case of a Boolean algebra, we observe that the corresponding homomorphism complex is isomorphic to the subcomplex of cubical cells in a permutahedron. Thus, this work can be interpreted as a generalization of the study of these complexes. We provide a detailed investigation when our poset is a product of chains, in which case we find an optimal discrete Morse matching and prove that the corresponding complex is torsion-free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-18T12:52:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal chains",
      "graded poset",
      "homomorphism complex construction",
      "optimal discrete morse matching",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}