2010/05/04 by Jonathan Ariel Barmak, Barmak, Jonathan Ariel · 1 citation
Mathematics · #06A07 #18B35. #55P10 #55U10 #57Q10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CO #msc:06A07 #msc:18B35. #msc:55P10 #msc:55U10 #msc:57Q10
paper · pdf · doi:10.48550/arxiv.1005.0538
7 pages.
arxiv created 2010/05/04 · openalex publication_date 2010/05/04 · arxiv updated 2010/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.