Combinatorics of Topological Posets: Homotopy Complementation Formulas

✍ Scribed by Rade T. Živaljević

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 313 KB
• Volume: 21
• Category: Article
• ISSN: 0196-8858
• DOI: 10.1006/aama.1998.0604

✦ Synopsis

We show that the well-known homotopy complementation formula of Bjorner and ẅ Ž . x Walker European J. Combin. 4 1983 , 11᎐19 admits several closely related Ž . generalizations on different classes of topological posets lattices . The utility of this technique is demonstrated on some classes of topological posets including the Ž . Ž . Grassmannian and configuration posets, G G R and exp X which were intron n w Ž . Ž . x duced and studied by V. Vassiliev St. Petersburg Math. J. 3 4 1991 , 108᎐115 .

Among other applications we present a reasonably complete description, in terms Ž m . of more standard spaces, of homology types of configuration posets exp S n which leads to a negative answer to a question of Vassiliev raised at the workshop ''Geometric Combinatorics' ' MSRI, February 1997. 1