On Quillen's Theorem A for posets

Details On Quillen's Theorem A for posets On Quillen's Theorem A for posets

2010-05-04

arxiv.org/abs/1005.0538v1

Mathematics

Combinatorics

7 pages.

Scientific paper

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.

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