A Thom Spectrum Model for $C_2$-Integral Brown--Gitler Spectra

TL;DR

This paper constructs a $C_2$-equivariant Thom spectrum model for Brown--Gitler spectra, demonstrating its multiplicative structure and potential for equivariant splittings similar to classical spectra.

Contribution

It introduces a new $C_2$-equivariant Thom spectrum model for Brown--Gitler spectra with multiplicative properties, extending classical nonequivariant results.

Findings

Established a $C_2$-equivariant Thom spectrum model.

Proved the model has a multiplicative property.

Potential applications in equivariant spectrum splittings.

Abstract

A Thom spectrum model for a $C_2$-equivariant analogue of integral Brown--Gitler spectra is established and shown to have a multiplicative property. The $C_2$-equivariant spectra constructed enjoy properties analogous to classical nonequivariant integral Brown--Gitler spectra and thus may prove useful for producing $C_2$-equivariant analogues of splittings of $BP \langle 1 \rangle \wedge BP \langle 1 \rangle$ and $bo \wedge bo.$