Collapsing along monotone poset maps

Dmitry N. Kozlov

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-8

Abstract:

We introduce the notion of nonevasive reduction and show that for any monotone poset map ϕ : P → P , the simplicial complex Δ ( P ) NE-reduces to Δ ( Q ) , for any Q ⊇ Fix ϕ .

As a corollary, we prove that for any order-preserving map ϕ : P → P satisfying ϕ ( x ) ≥ x , for any x ∈ P , the simplicial complex Δ ( P ) collapses to Δ ( ϕ ( P ) ) . We also obtain a generalization of Crapo's closure theorem.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:079858

DOI: 10.1155/IJMMS/2006/79858

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