A SUSPENSION LEMMA FOR BOUNDED POSETS

JÖRG RAMBAU

Abstract. Let P and Q be bounded posets. In this note, a lemma is introduced that provides a set of sufficient conditions for the proper part of P being homotopy equivalent to the suspension of the proper part of Q. An application of this lemma is a unified proof of the sphericity of the higher Bruhat orders under both inclusion order (a known proved earlier by Ziegler) and single step inclusion order (which was not previously known).