Realizing compatible pairs of transfer systems by combinatorial N_∞-operads

2025/10/30 by Chan, David, Cho, Myungsin, Mehrle, David +4
#06A07 #18M60 #55P91 #55U35 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.26047

Abstract

We investigate how the notions of pairings of operads of May and compatible pairs of indexing systems of Blumberg--Hill relate via the correspondence between indexing systems and N_∞-operads. We show that a pairing of operads induces a pairing on the associated indexing systems. Conversely, we show that in many cases, compatible pairs of indexing systems can be realized by a pairing of N_∞-operads.

Citations

• The Formal Context of Saturated Transfer Systems on Finite Abelian Groups
• Uniquely compatible transfer systems for cyclic groups of order p^rq^s
• Counting compatible indexing systems for C_pⁿ
• Saturated and linear isometric transfer systems for cyclic groups of order p^mqⁿ
• Bi-incomplete Tambara functors
• Operadic multiplications in equivariant spectra, norms, and transfers

Related

• The combinatorics of N_∞ operads for C_qpⁿ and D_pⁿ
• Realizing Transfer Systems as Suboperads of Coinduced Operads
• Categorifying the algebra of indexing systems
• Counting compatible indexing systems for C_pⁿ
• Combinatorial homotopy theory for operads