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On Generalized Heawood Inequalities for Manifolds: A Van Kampen-Flores-type Nonembeddability Result

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10320318" target="_blank" >RIV/00216208:11320/15:10320318 - isvavai.cz</a>

  • Result on the web

    <a href="http://drops.dagstuhl.de/opus/volltexte/2015/5125/" target="_blank" >http://drops.dagstuhl.de/opus/volltexte/2015/5125/</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.476" target="_blank" >10.4230/LIPIcs.SOCG.2015.476</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On Generalized Heawood Inequalities for Manifolds: A Van Kampen-Flores-type Nonembeddability Result

  • Original language description

    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 aclosed 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 Heawoodinequality 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

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

  • Continuities

    S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2015

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Proceedings of the 31st International Symposium on Computational Geometry (SoCG 2015)

  • ISBN

    978-3-939897-83-5

  • ISSN

    1868-8969

  • e-ISSN

  • Number of pages

    15

  • Pages from-to

    476-490

  • Publisher name

    LIPICS

  • Place of publication

    Dagstuhl

  • Event location

    Eindhoven

  • Event date

    Jun 22, 2015

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article