---
res:
  bibo_abstract:
  - 'The fact that the complete graph K5 does not embed in the plane has been generalized
    in two independent directions. On the one hand, the solution of the classical
    Heawood problem for graphs on surfaces established that the complete graph Kn
    embeds in a closed surface M (other than the Klein bottle) if and only if (n−3)(n−4)
    ≤ 6b1(M), where b1(M) is the first Z2-Betti number of M. On the other hand, van
    Kampen and Flores proved that the k-skeleton of the n-dimensional simplex (the
    higher-dimensional analogue of Kn+1) embeds in R2k if and only if n ≤ 2k + 1.
    Two decades ago, Kühnel conjectured that the k-skeleton of the n-simplex embeds
    in a compact, (k − 1)-connected 2k-manifold with kth Z2-Betti number bk only if
    the following generalized Heawood inequality holds: (k+1 n−k−1) ≤ (k+1 2k+1)bk.
    This is a common generalization of the case of graphs on surfaces as well as the
    van Kampen–Flores theorem. In the spirit of Kühnel’s conjecture, we prove that
    if the k-skeleton of the n-simplex embeds in a compact 2k-manifold with kth Z2-Betti
    number bk, then n ≤ 2bk(k 2k+2)+2k+4. This bound is weaker than the generalized
    Heawood inequality, but does not require the assumption that M is (k−1)-connected.
    Our results generalize to maps without q-covered points, in the spirit of Tverberg’s
    theorem, for q a prime power. Our proof uses a result of Volovikov about maps
    that satisfy a certain homological triviality condition.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Xavier
      foaf_name: Goaoc, Xavier
      foaf_surname: Goaoc
  - foaf_Person:
      foaf_givenName: Isaac
      foaf_name: Mabillard, Isaac
      foaf_surname: Mabillard
      foaf_workInfoHomepage: http://www.librecat.org/personId=32BF9DAA-F248-11E8-B48F-1D18A9856A87
  - foaf_Person:
      foaf_givenName: Pavel
      foaf_name: Paták, Pavel
      foaf_surname: Paták
  - foaf_Person:
      foaf_givenName: Zuzana
      foaf_name: Patakova, Zuzana
      foaf_surname: Patakova
      foaf_workInfoHomepage: http://www.librecat.org/personId=48B57058-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-3975-1683
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Tancer, Martin
      foaf_surname: Tancer
      foaf_workInfoHomepage: http://www.librecat.org/personId=38AC689C-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1191-6714
  - foaf_Person:
      foaf_givenName: Uli
      foaf_name: Wagner, Uli
      foaf_surname: Wagner
      foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1494-0568
  bibo_doi: 10.1007/s11856-017-1607-7
  bibo_issue: '2'
  bibo_volume: 222
  dct_date: 2017^xs_gYear
  dct_identifier:
  - UT:000415195500009
  dct_language: eng
  dct_publisher: Springer@
  dct_title: 'On generalized Heawood inequalities for manifolds: A van Kampen–Flores
    type nonembeddability result@'
...