Commutativity properties of Quinn spectra
Algebraic Topology
2025-04-02 v3
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.
Keywords
Cite
@article{arxiv.1304.4759,
title = {Commutativity properties of Quinn spectra},
author = {Gerd Laures and James E. McClure},
journal= {arXiv preprint arXiv:1304.4759},
year = {2025}
}
Comments
86 pages; final version