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Subadditivity of shifts, Eilenberg-Zilber shuffle products and homology of lattices
- Publication Year :
- 2024
-
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.
- Subjects :
- Mathematics - Commutative Algebra
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.16643
- Document Type :
- Working Paper