On Quillenʼs Theorem A for posets
Copyright policy )On Quillenʼs Theorem A for posets
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.
7 pages.
Simple homotopy equivalences, Combinatorial aspects of simplicial complexes, fiber lemma, simplicial complexes, simple homotopy equivalences, Theoretical Computer Science, posets, Posets, FOS: Mathematics, Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc., Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Homotopy equivalences, homotopy equivalences, Simplicial complexes, Ordered sets, Fiber Lemma, Computational Theory and Mathematics, Algebraic combinatorics, 55U10, 06A07, 55P10, 57Q10, 18B35., Combinatorics (math.CO), Homotopy equivalences in algebraic topology
Simple homotopy equivalences, Combinatorial aspects of simplicial complexes, fiber lemma, simplicial complexes, simple homotopy equivalences, Theoretical Computer Science, posets, Posets, FOS: Mathematics, Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc., Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Homotopy equivalences, homotopy equivalences, Simplicial complexes, Ordered sets, Fiber Lemma, Computational Theory and Mathematics, Algebraic combinatorics, 55U10, 06A07, 55P10, 57Q10, 18B35., Combinatorics (math.CO), Homotopy equivalences in algebraic topology
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