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Mathematics > Commutative Algebra
Title: Subadditivity of shifts, Eilenberg-Zilber shuffle products and homology of lattices
(Submitted on 25 Apr 2024 (v1), last revised 2 May 2024 (this version, v2))
Abstract: We show that the maximal shifts in the minimal free resolution of the quotients of a polynomial ring by a monomial ideal are subadditive as a function of the homological degree. This answers a question that has received some attention in recent years. To do so, we define and study a new model for the homology of posets, given by the so called synor complex. We also introduce an Eilenberg-Zilber type shuffle product on the simplicial chain complex of lattices.
Combining these concepts we prove that the existence of a non-zero homology class for a lattice forces certain non-zero homology classes in lower intervals. This result then translates into properties of the minimal free resolution. In particular, it implies a generalization of the original question.
Submission history
From: Karim Alexander Adiprasito [view email][v1] Thu, 25 Apr 2024 14:31:20 GMT (33kb)
[v2] Thu, 2 May 2024 11:29:21 GMT (33kb)
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