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
—