Handbook of combinatorics (vol. 2)
On Quillen's Theorem A for posets
Journal of Combinatorial Theory Series A
Geometry in the space of persistence modules
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Two theorems are proved. One concerns coverings of a simplicial complex Δ by subcomplexes. It is shown that if every t-wise intersection of these subcomplexes is (k- t + 1)-connected, then for j≤k there are isomorphisms πj(Δ)≅πj(N) of homotopy groups of Δ and of the nerve N of the covering.The other concerns poset maps f : P → Q. It is shown that if all fibers f-1(Q≤q) are k- connected, then f induces isomorphisms of homotopy groups πj(P)≅πj(Q), for all j ≤ k.