Chains on suspension spectra

TL;DR

This paper introduces a homological analogue of Sullivan's rational de Rham complex for simplicial sets, extending it to simplicial symmetric spectra with strong categorical properties to facilitate future applications.

Contribution

It develops a homological version of Sullivan's de Rham complex and generalizes it to simplicial symmetric spectra, enhancing categorical features for broader applications.

Findings

New homological de Rham complex for simplicial sets

Extension to simplicial symmetric spectra with strong categorical properties

Potential for simplifying applications in algebraic topology

Abstract

We define and study a homological version of Sullivan's rational de Rham complex for simplicial sets. This new functor can be generalised to simplicial symmetric spectra and in that context it has excellent categorical properties which promise to make a number of interesting applications much more straightforward.