Partial monoids and Dold-Thom functors

TL;DR

This paper introduces a new way to construct Dold-Thom functors directly from spectra using partial monoids, extending the classical framework of symmetric products and homology theories.

Contribution

It provides a novel construction of Dold-Thom functors from spectra via partial monoids, bypassing traditional $ ext{Γ}$-space methods.

Findings

Constructed partial monoids corresponding to spectra.

Established a direct link between spectra and Dold-Thom functors.

Extended the framework of infinite symmetric products.

Abstract

Dold-Thom functors are generalizations of infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that for any connective homology theory, the machinery of $\Gamma$-spaces produces the corresponding linear Dold-Thom functor. In this note we construct such functors directly from spectra by exhibiting a partial monoid corresponding to a spectrum.