Commutativity properties of Quinn spectra

Abstract

We give a simple sufficient condition for Quinn's "bordism-type" spectra to be weakly equivalent to commutative symmetric ring spectra. We also show that the symmetric signature is (up to weak equivalence) a monoidal transformation between symmetric monoidal functors, which implies that the Sullivan-Ranicki orientation of topological bundles is represented by a ring map between commutative symmetric ring spectra. In the course of proving these statements we give a new description of symmetric L theory which may be of independent interest.

86 pages; final version

References in corpus (2)

• Rings, modules, and algebras in infinite loop space theory
• The total surgery obstruction revisited

Cited by in corpus (2)

• On the homotopy type of L-spectra of the integers
• On the Relation between K- and L-Theory of $C^{\ast }$-Algebras