Abstract

We introduce the notion of nonevasive reduction and show that for any monotone poset map ϕ:PP, the simplicial complex Δ(P) NE-reduces to Δ(Q), for any QFixϕ.As a corollary, we prove that for any order-preserving map ϕ:PP satisfying ϕ(x)x, for any xP, the simplicial complex Δ(P) collapses to Δ(ϕ(P)). We also obtain a generalization of Crapo's closure theorem.