2025/10/27 by Laubie, Paul
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2510.23547
We show a variation of the usual homological freeness criterion for operadic modules over a Koszul operad. We then apply this result to decorated partition posets for some operads, showing that their augmentation is Cohen-Macaulay and computing its homology. This work answers several open questions asked by Bérénice Delcroix-Oger and Clément Dupont in a recent article.