Abstract
AbstractWe study the indexing systems that correspond to equivariant Steiner and linear isometries operads. When G is a finite abelian group, we prove that a G-indexing system is realized by a Steiner operad if and only if it is generated by cyclic G-orbits. When G is a finite cyclic group, whose order is either a prime power or a product of two distinct primes greater than 3, we prove that a G-indexing system is realized by a linear isometries operad if and only if it satisfies Blumberg and Hill’s horn-filling condition. We also repackage the data in an indexing system as a certain kind of partial order. We call these posets transfer systems, and develop basic tools for computing with them.
Publisher
Cambridge University Press (CUP)
Reference16 articles.
1. Iterated loop spaces and the
2. Incomplete Tambara functors
3. Equivariant multiplicative closure
4. 15. Rubin, J. , Categorifying the algebra of indexing systems. Preprint arXiv:1909.11739.
5. 10. Hill, M. A. and Hopkins, M. J. , Equivariant symmetric monoidal structure. Preprint arXiv:1610.03114.
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Bi-incomplete Tambara functors as
-commutative monoids;Tunisian Journal of Mathematics;2024-01-20
2. Counting compatible indexing systems for
Cpn;Orbita Mathematicae;2024-01-01
3. Lifting N∞ operads from conjugacy
data;Tunisian Journal of Mathematics;2023-11-02
4. Model structures on finite total orders;Mathematische Zeitschrift;2023-06-13
5. Global N∞$N_\infty$‐operads;Bulletin of the London Mathematical Society;2023-01-09