Defines rank-filtered subcomplexes of order complexes of graded posets and proves their homology matches manifold homology except in top degree, plus shellability and wedge-of-spheres homotopy types for shellable and geometric semilattice cases.
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Filtered order complexes and magnitude homology of finite graded posets
Defines rank-filtered subcomplexes of order complexes of graded posets and proves their homology matches manifold homology except in top degree, plus shellability and wedge-of-spheres homotopy types for shellable and geometric semilattice cases.