Singularities and Quinn spectra

TL;DR

This paper introduces singularities into Quinn spectra, allowing for the study of spectra with prescribed singularities and explicit construction of important examples like Morava K-theories and L-theory with singularities.

Contribution

It develops a framework for incorporating singularities into Quinn spectra and constructs explicit representatives for key spectra, along with a spectral sequence for bordism computations.

Findings

Constructed representatives for Morava K-theories with singularities

Developed a spectral sequence for bordism groups with singularities

Analyzed product structures in the context of singular Quinn spectra

Abstract

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.