Commutativity properties of Quinn spectra

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

Singularities and Quinn spectra

We introduce singularities to Quinn spectra. It enables us to talk about ads with prescribed singularities and to explicitly construct representatives for prominent spectra like Morava $K$-theories or for $L$-theory with singularities. We develop a spectral sequence for the computation of the associated bordism groups and investigate product structures in the presence of singularities.Comment: final published versio

The topological q-expansion principle

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.Includes bibliographical references (p. 49-50).by Gerd Laures.Ph.D