{
  "id": "math/9904089",
  "version": "v1",
  "published": "1999-04-18T07:31:06.000Z",
  "updated": "1999-04-18T07:31:06.000Z",
  "title": "On Homology of Virtual Braids and Burau Representation",
  "authors": [
    "V. V. Vershinin"
  ],
  "comment": "17 pages, AMSTeX, 17 figures",
  "journal": "J. Knot Theory Ramifications 10 (2001), no. 5, 795-812",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Virtual knots arise in the study of Gauss diagrams and Vassiliev invariants of usual knots. Virtual braids correspond naturally to virtual knots. We consider the group of virtual braids on n strings VB_n and its Burau representation, in particular we study their homological properties. We prove that the plus-construction of the classifying space of the virtual braid group on the infinite number of strings is an infinite loop space which is equivalent to a product of Q(S^0), S^1 and an infinite loop space Y. Connections with the K-functor of the integers are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-04-18T07:31:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J05",
      "20F36",
      "20F38",
      "18D10",
      "55P35"
    ],
    "keywords": [
      "burau representation",
      "infinite loop space",
      "virtual braids correspond",
      "virtual braid group",
      "virtual knots arise"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......4089V"
    }
  }
}