{
  "id": "1106.6176",
  "version": "v1",
  "published": "2011-06-30T10:20:55.000Z",
  "updated": "2011-06-30T10:20:55.000Z",
  "title": "Geometric coincidence results from multiplicity of continuous maps",
  "authors": [
    "R. N. Karasev"
  ],
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "In this paper we study geometric coincidence problems in the spirit of the following problems by B. Gr\\\"unbaum: How many affine diameters of a convex body in $\\mathbb R^n$ must have a common point? How many centers (in some sense) of hyperplane sections of a convex body in $\\mathbb R^n$ must coincide? One possible approach to such problems is to find topological reasons for multiple coincidences for a continuous map between manifolds of equal dimension. In other words, we need topological estimates for the multiplicity of a map. In this work examples of such estimates and their geometric consequences are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-30T10:20:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "55M20"
    ],
    "keywords": [
      "geometric coincidence results",
      "continuous map",
      "multiplicity",
      "convex body",
      "study geometric coincidence problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.6176K"
    }
  }
}