Multiplicative properties of Quinn spectra

Abstract

We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's functor from bordism-type theories to spectra lifts to the category of symmetric spectra. We also give a new account of the foundations.

arXiv comment52 pages. Appendix added on the Quinn and Thom versions of MTop. Set-theoretic discussions added to show that certain objects are really sets and not classes. Various minor technical improvements