Equivariant Multiplicative Closure

Abstract

This paper describes an issue that arises when inverting elements of the homotopy groups of an equivariant commutative ring. Equivariant commutative rings possess an enhanced multiplicative structure arising from the presence of "indexed products" (products indexed by a set with a non-trivial action of the group). The formation of the "multiplicative closure" of a set must be altered in order to accomodate this structure, and the result of localizing an equivariant commutative ring can have an unexpected homotopy type.