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Abstract
In this paper, we consider the iterated trimming complex associated to data yielding a complex of length 3. We compute an explicit algebra structure in this complex in terms of the algebra structures of the associated input data. Moreover, it is shown that many of these products become trivial after descending to homology. We apply these results to the problem of realizability for Tor-algebras of grade 3 perfect ideals, and show that under mild hypotheses, the process of “trimming” an ideal preserves Tor-algebra class. In particular, we construct new classes of ideals in arbitrary regular local rings defining rings realizing Tor-algebra classes G(r) and H(p,q) for a prescribed set of homological data.
Document Type
Article
Publication Date
9-1-2022
Digital Object Identifier (DOI)
10.1016/j.jpaa.2022.107053
Archival?
Archival
Repository Citation
VandeBogert, Keller, "DG structure on length 3 trimming complexes and applications to Tor algebras" (2022). Mathematics Faculty Publications. 72.
https://uknowledge.uky.edu/math_facpub/72
Notes/Citation Information
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