Thom Complexes and the Spectrum tmf

TL;DR

This paper investigates the realization of certain spectra as Thom spectra, demonstrating that the spectrum tmf at the prime 2 cannot be realized as an E_1 Thom spectrum, extending previous results.

Contribution

It proves that the spectrum tmf_{(2)} cannot be realized as an E_1 Thom spectrum, using techniques related to earlier work on bu and bo spectra.

Findings

tmf_{(2)} cannot be realized as an E_1 Thom spectrum

Extends techniques from bu and bo to tmf spectrum

Provides insights into the structure of tmf spectrum

Abstract

Many interesting spectra can be constructed as Thom spectra of easily constructed bundles. Mahowald showed that $\mathit{bu}$ and $\mathit{bo}$ cannot be realized as $E_1$ Thom spectra. We use related techniques to show that $\mathit{tmf}_{(2)}$ also cannot be realized as an $E_1$ Thom spectrum.