Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-98-05021-7
MathSciNet review: 1621965
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 05E99, 06A09, 06B99

Retrieve articles in all journals with MSC (1991): 05E99, 06A09, 06B99


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
Email: kozlov@math.mit.edu, kozlov@math.kth.se

DOI: https://doi.org/10.1090/S0002-9939-98-05021-7
Received by editor(s): February 25, 1997
Communicated by: Jeffry Kahn
Article copyright: © Copyright 1998 American Mathematical Society