On Quillen's Theorem A for posets
2011 (English)In: Journal of Combinatorial Theory. Series A, ISSN 0097-3165, Vol. 118, no 8, 2445-2453 p.Article in journal (Refereed) Published
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.
Fiber lemma, Homotopy equivalences, Posets, Simple homotopy equivalences, Simplicial complexes
IdentifiersURN: urn:nbn:se:kth:diva-151129DOI: 10.1016/j.jcta.2011.06.008ISI: 000294983300016ScopusID: 2-s2.0-79959551137OAI: oai:DiVA.org:kth-151129DiVA: diva2:748958
FunderKnut and Alice Wallenberg Foundation, KAW 2005.0098
QC 201409222014-09-222014-09-152015-10-09Bibliographically approved