Saturated and linear isometric transfer systems for cyclic groups of order p^mqⁿ

2021/09/16 by Hafeez, Usman, Marcus, Peter, Ormsby, Kyle +1 · 4 citations
#55P91 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.08210

Abstract

Transfer systems are combinatorial objects which classify N_∞ operads up to homotopy. By results of A. Blumberg and M. Hill, every transfer system associated to a linear isometries operad is also saturated (closed under a particular two-out-of-three property). We investigate saturated and linear isometric transfer systems with equivariance group C_p^mqⁿ, the cyclic group of order p^mqⁿ for p,q distinct primes and m,n≥ 0. We give a complete enumeration of saturated transfer systems for C_p^mqⁿ. We also prove J. Rubin's saturation conjecture for C_pqⁿ; this says that every saturated transfer system is realized by a linear isometries operad for p,q sufficiently large (greater than 3 in this case).

Cited by

• Left and right Bousfield localization on lattices
• The Formal Context of Saturated Transfer Systems on Finite Abelian Groups
• Realizing compatible pairs of transfer systems by combinatorial N_∞-operads
• Enumerating submonoids of finite commutative monoids

Related

• Realization of saturated transfer systems on cyclic groups of order pⁿq^m by linear isometries N_∞-operads
• Equivariant linear isometries operads over Abelian groups
• The Formal Context of Saturated Transfer Systems on Finite Abelian Groups
• The combinatorics of N_∞ operads for C_qpⁿ and D_pⁿ
• Uniquely compatible transfer systems for cyclic groups of order p^rq^s