Tolerance complexes preserve Lerayness
Tolerance-Leray conjecture. Then Tt(K)\mathcal{T}_{t}(K)Tt(K) is (η(d+1,t+1)−1)(\eta(d+1,t+1)-1)(η(d+1,t+1)−1)-Leray.
The representability bound for simplicial complexes with bounded Leray number
Representability bound conjecture. If h(X)≤dh(X)\leq dh(X)≤d for d≥1d\geq 1d≥1, then
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