Abstract

. We show that the well known homotopy complementation formula of Bjorner and Walker admits several closely related generalizations on different classes of topological posets (lattices). The utility of this technique is demonstrated on some classes of topological posets including the Grassmannian and configuration posets, e Gn (R) and exp n (X) which were introduced and studied by V. Vassiliev. Among other applications we present a reasonably complete description, in terms of more standard spaces, of homology types of configuration posets exp n (S m ) which leads to a negative answer to a question of Vassilev raised at the workshop "Geometric Combinatorics" (MSRI, February 1997). 1. Introduction One of the objectives of this paper is to initiate the study of topological (continuous) posets and their order complexes from the point of view of Geometric Combinatorics. Recall that finite or more generally locally finite partially ordered sets (posets) already occupy one of privileged ...

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