Homotopy type of posets and lattice complementation |
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Authors: | Anders Björner |
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Affiliation: | Department of Mathematics, University of Stockholm, Box 6701, S-11385 Stockholm, Sweden |
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Abstract: | This paper is concerned with homotopy properties of partially ordered sets, in particular contractibility. The main result is that a noncomplemented lattice with deleted bounds is contractible. The paper also presents (i) the homology of final sets and cutsets, (ii) a generalization to posets of Rota's crosscut theorem, (iii) contractibility proofs for some classes of posets of interest in fixed point theory, and (iv) a simple characterization of the Cohen-Macaulay property for dismantlable lattices. |
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