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On Quillen's Theorem A for posets
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: Journal of Combinatorial Theory. Series A, ISSN 0097-3165, Vol. 118, no 8, 2445-2453 p.Article in journal (Refereed) Published
Abstract [en]

A theorem of McCord of 1966 and Quillen's Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We give an alternative elementary proof of this result and we deduce also a stronger statement: under the hypotheses of the theorem, the map is not only a homotopy equivalence but a simple homotopy equivalence. This leads then to stronger formulations of the simplicial version of Quillen's Theorem A, the Nerve Lemma and other known results. In particular we establish a conjecture of Kozlov on the simple homotopy type of the crosscut complex and we improve a well-known result of Cohen on contractible mappings.

Place, publisher, year, edition, pages
2011. Vol. 118, no 8, 2445-2453 p.
Keyword [en]
Fiber lemma, Homotopy equivalences, Posets, Simple homotopy equivalences, Simplicial complexes
National Category
URN: urn:nbn:se:kth:diva-151129DOI: 10.1016/j.jcta.2011.06.008ISI: 000294983300016ScopusID: 2-s2.0-79959551137OAI: diva2:748958
Knut and Alice Wallenberg Foundation, KAW 2005.0098

QC 20140922

Available from: 2014-09-22 Created: 2014-09-15 Last updated: 2015-10-09Bibliographically approved

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Barmak, Jonathan Ariel
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