A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit <a rel="external noopener" href="https://link.springer.com/content/pdf/10.1007/s41468-021-00069-z.pdf?error=cookies_not_supported&code=8a6512b6-8e27-4839-949d-17a4b0698f52">the original URL</a>. The file type is <code>application/pdf</code>.
The Rado simplicial complex
<span title="2021-05-06">2021</span>
<i title="Springer Science and Business Media LLC">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c5jvinnaofg2pnrpaxbxvqkocq" style="color: black;">Journal of Applied and Computational Topology</a>
</i>
Preserved Fulltext
AbstractWe study a remarkable simplicial complex X on countably many vertexes. X is universal in the sense that any countable simplicial complex is an induced subcomplex of X. Additionally, X is homogeneous, i.e. any two isomorphic finite induced subcomplexes are related by an automorphism of X. We prove that X is the unique simplicial complex which is both universal and homogeneous. The 1-skeleton of X is the well-known Rado graph. We show that a random simplicial complex on countably many
<span class="external-identifiers">
<a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s41468-021-00069-z">doi:10.1007/s41468-021-00069-z</a>
<a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ko7ptfuobzctngjfrjwjew4ptq">fatcat:ko7ptfuobzctngjfrjwjew4ptq</a>
</span>
more »
... exes is isomorphic to X with probability 1. We prove that the geometric realisation of X is homeomorphic to an infinite dimensional simplex. We observe several curious properties of X, for example we show that X is robust, i.e. removing any finite set of simplexes leaves a simplicial complex isomorphic to X. The robustness of X leads to the hope that suitable finite approximations of X can serve as models for very resilient networks in real life applications. In a forthcoming paper (Even-Zohar et al. Ample simplicial complexes, arXiv:2012.01483, 2020) we study finite approximations to the Rado complex, they can potentially be useful in real life applications due to their structural stability.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210718052152/https://link.springer.com/content/pdf/10.1007/s41468-021-00069-z.pdf?error=cookies_not_supported&code=8a6512b6-8e27-4839-949d-17a4b0698f52" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext">
<button class="ui simple right pointing dropdown compact black labeled icon button serp-button">
<i class="icon ia-icon"></i>
Web Archive
[PDF]
<div class="menu fulltext-thumbnail">
<img src="https://blobs.fatcat.wiki/thumbnail/pdf/b7/8f/b78fdaeb01128f3180e7b7ada785191d404e3c34.180px.jpg" alt="fulltext thumbnail" loading="lazy">
</div>
</button>
</a>
<a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s41468-021-00069-z">
<button class="ui left aligned compact blue labeled icon button serp-button">
<i class="unlock alternate icon" style="background-color: #fb971f;"></i>
springer.com
</button>
</a>