COLLAPSING ALONG MONOTONE POSET MAPS

We introduce the notion of nonevasive reduction and show that for any monotone poset map :PP, the simplicial complex (P) NE-reduces to (Q), for any QFix. As a corollary, we prove that for any order-preserving map :PP satisfying (x)x, for any xP, the simplicial complex (P) collapses to ((P)). We also...

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Bibliographic Details
Published inInternational Journal of Mathematics and Mathematical Sciences Vol. 2006; pp. 1 - 8
Main Author Kozlov, Dmitry N.
Format Journal Article
LanguageEnglish
Published Hindawi Limiteds 2006
Wiley
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Summary:We introduce the notion of nonevasive reduction and show that for any monotone poset map :PP, the simplicial complex (P) NE-reduces to (Q), for any QFix. As a corollary, we prove that for any order-preserving map :PP satisfying (x)x, for any xP, the simplicial complex (P) collapses to ((P)). We also obtain a generalization of Crapo's closure theorem.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0161-1712
1687-0425
DOI:10.1155/IJMMS/2006/79858