Collapsing along monotone poset maps
Open Access
- 1 January 2006
- journal article
- Published by Wiley in International Journal of Mathematics and Mathematical Sciences
- Vol. 2006 (1)
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⊇Fixϕ.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.Keywords
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Funding Information
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (PP002-102738/1)
- ETH-Zürich (PP002-102738/1)
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