Abstract :
We study several standard combinatorial constructions on simplicial complexes (e.g., barycentric subdivision, join). We are interested in the question whether these constructions preserve the properties evasiveness and collapsibility. In particular, we are interested in simplicial complexes that are order complexes of posets. We show that the order complex of the direct product of two posets is collapsible (resp., non-evasive) if the order complex of each factor is collapsible (resp., non-evasive). More surprisingly, we show that if Δ is a collapsible complex then its barycentric subdivision sd(Δ) is non-evasive.
