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Commutativity properties of Quinn spectra

Commutativity properties of Quinn spectra

We give a simple sufficient condition for Quinnā€™s ā€˜bordism-typeā€™ 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 Sullivanā€“Ranicki orientation of topological bundles is represented by ā€¦