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Breaking up Simplicial Homology and Subadditivity of Syzygies

We consider the following question: if a simplicial complex $Δ$ has $d$-homology, then does the corresponding $d$-cycle always induce cycles of smaller dimension that are not boundaries in $Δ$? We provide an answer to this question in a fixed dimension. We use the breaking of homology to show the subadditivity property for the maximal degrees of syzygies of monomial ideals in a fixed homological degree.

preprint2022arXivOpen access
Sara FaridiMayada Shahada
math.AC
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Sara FaridiMayada Shahada

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