Algebraic shifting increases relative homology

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Algebraic shifting increases relative homology

We show that algebraically shifting a pair of simplicial complexes weakly increases their relative homology Betti numbers in every dimension. More precisely, let ∆(K) denote the algebraically shifted complex of simplicial complex K, and let β j (K, L) = dim k H j (K, L; k) be the dimension of the jth reduced relative homology group over a field k of a pair of simplicial complexes L ⊆ K. Then β ...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2000

ISSN: 0012-365X

DOI: 10.1016/s0012-365x(00)00151-5