Brown–Gitler spectrum

In the mathematical discipline of topology, the Brown–Gitler spectrum is a spectrum whose cohomology is a certain cyclic module over the Steenrod algebra.^[1]

Brown–Gitler spectra are defined by the isomorphism:^[2]

${\displaystyle \Sigma ^{n}A/\{\operatorname {Sq} ^{i}:2i>n\}A\cong G(n).}$

History

The concept was introduced by mathematicians Edgar H. Brown and Samuel Gitler in a 1973 paper.^[1][3]

In topology, Brown–Gitler spectrum is related to the concepts of the Segal conjecture (proven in 1984) and the Burnside ring.^[4]

Applications

Brown–Gitler spectra have had many important applications in homotopy theory.^[5]