Dimension gaps between representability and collapsibility

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F09%3A00207115" target="_blank" >RIV/00216208:11320/09:00207115 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Dimension gaps between representability and collapsibility
Original language description
A simplicial complex K is called d-representable if it is the nerve of a collection of convex sets in R^d; K is d-collapsible if it can be reduced to an empty complex by repeatedly removing a face of dimension at most d - 1 that is contained in a uniquemaximal face; and K is d-Leray if every induced subcomplex of K has vanishing homology of dimension d and larger. It is known that d-representable implies d-collapsible implies d-Leray, and no two of these notions coincide for d }= 2. The famous Helly theorem and other important results in discrete geometry can be regarded as results about d-representable complexes, and in many of these results, 'd-representable' in the assumption can be replaced by 'd-collapsible' or even 'd-Leray.' Zbytek anotace chybí kvůli limitu počtu znaků.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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