On the Homological Dimension of Lattices

نویسنده

Roy Meshulam

چکیده

Let L be a finite lattice and let L̂ = L − {0̂, 1̂}. It is shown that if the order complex ∆(L̂) satisfies H̃k−2 ( ∆(L̂) ) 6= 0 then |L| ≥ 2k. Equality |L| = 2k holds iff L is isomorphic to the Boolean lattice {0, 1}k.

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