Topology of the view complex
Dmitry N. Kozlov · Homology Homotopy and Applications · 2015
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 View n can be collapsed to the well-known complex χ(Δ n ), called standard chromatic subdivision of a simplex, and that χ(Δ 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.