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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 79858, 8 pages
http://dx.doi.org/10.1155/IJMMS/2006/79858

Collapsing along monotone poset maps

Institute of Theoretical Computer Science, Swiss Federal Institute of Technology Zurich, Zurich 8092, Switzerland

Received 21 March 2005; Revised 13 September 2005; Accepted 12 February 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.