Geodesic
Topology of the view complex
Homology, homotopy, and applications, Tome 17 (2015) no. 1, pp. 307-319.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper we consider a family of simplicial complexes, which we call the view complexes. Our choice of objects of study is motivated by theoretical distributed computing, since the view complex is a key simplicial construction used for protocol complexes in the snapshot computational model. We show that the view complex $\textrm{View}^n$ can be collapsed to the well-known complex $\chi(\Delta^n)$, called standard chromatic subdivision of a simplex, and that $\chi(\Delta^n)$ is itself collapsible. Furthermore, we show that the collapses can be performed simultaneously in entire orbits of the natural symmetric group action. Our results yield a purely combinatorial and constructive understanding of the topology of view complexes, at the same time as they enhance our knowledge about the standard chromatic subdivision of a simplex.
DOI : 10.4310/HHA.2015.v17.n1.a15
Classification : 57Q05, 68Q85
Keywords: collapses, distributed computing, combinatorial algebraic topology, immediate snapshot, read-write protocols 
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Dmitry N. Kozlov. Topology of the view complex. Homology, homotopy, and applications, Tome 17 (2015) no. 1, pp. 307-319. doi : 10.4310/HHA.2015.v17.n1.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2015.v17.n1.a15/

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