---
res:
  bibo_abstract:
  - 'The fact that the complete graph K_5 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 K_n
    embeds in a closed surface M if and only if (n-3)(n-4) is at most 6b_1(M), where
    b_1(M) is the first Z_2-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 K_{n+1}) embeds in R^{2k} if and only if n is less or equal to 2k+2.
    Two decades ago, Kuhnel conjectured that the k-skeleton of the n-simplex embeds
    in a compact, (k-1)-connected 2k-manifold with kth Z_2-Betti number b_k only if
    the following generalized Heawood inequality holds: binom{n-k-1}{k+1} is at most
    binom{2k+1}{k+1} b_k. This is a common generalization of the case of graphs on
    surfaces as well as the Van Kampen--Flores theorem. In the spirit of Kuhnel''s
    conjecture, we prove that if the k-skeleton of the n-simplex embeds in a 2k-manifold
    with kth Z_2-Betti number b_k, then n is at most 2b_k binom{2k+2}{k} + 2k + 5.
    This bound is weaker than the generalized Heawood inequality, but does not require
    the assumption that M is (k-1)-connected. 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: 10.4230/LIPIcs.SOCG.2015.476
  bibo_volume: '34 '
  dct_date: 2015^xs_gYear
  dct_language: eng
  dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
  dct_title: 'On generalized Heawood inequalities for manifolds: A Van Kampen–Flores-type
    nonembeddability result@'
...