DETECTING STEINER AND LINEAR ISOMETRIES OPERADS

Abstract

Abstract We 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.

Locations

• Glasgow Mathematical Journal - View - PDF