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Order complexes of noncomplemented lattices are nonevasive

Author: Dmitry N. Kozlov
Journal: Proc. Amer. Math. Soc. 126 (1998), 3461-3465
MSC (1991): Primary 05E99, 06A09, 06B99
MathSciNet review: 1621965
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Abstract: We prove the following theorem: Let ${\mathcal{L}}$ be a finite lattice, $x\!\in\!\bar {\mathcal{L}}$.
Assume $B$ is a set of elements of ${\mathcal{L}}$ which includes all complements of $x$ and is included in the set of all upper (lower) semicomplements of $x$. Then $\Delta (\overline {{\mathcal{L}}\setminus B})$ is nonevasive, in particular collapsible. This generalizes results of several previous papers, where, in different generalities, it has been proved that the mentioned complex is contractible.

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Additional Information

Dmitry N. Kozlov
Affiliation: Department of Mathematics, 2-392, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Address at time of publication: Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540

Received by editor(s): February 25, 1997
Communicated by: Jeffry Kahn
Article copyright: © Copyright 1998 American Mathematical Society

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