Brown–Gitler spectrum explained
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]
\SigmanA/\{\operatorname{Sq}i:2i>n\}A\congG(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]
Notes and References
- Web site: Brown–Gitler spectrum in nLab.
- Web site: Brown–Gitler Spectra.
- Edgar H. Jr. . Brown. Edgar H. Brown. Samuel. Gitler. Samuel Gitler Hammer . A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra. . 12 . 1973. 3. 283–295. 0391071. 10.1016/0040-9383(73)90014-1.
- Book: Recent Developments in Algebraic Topology: A Conference to Celebrate Sam Gitler's 70th Birthday, December 3–6, 2003, San Miguel de Allende, México. Samuel. Gitler. Samuel Gitler Hammer . Jesús. González. 1 January 2006. American Mathematical Society. 9780821836767. Google Books.
- 2047129. Integral Brown–Gitler Spectra. Fred R.. Cohen. Donald M.. Davis. Paul G.. Goerss. Mark E.. Mahowald. Proceedings of the American Mathematical Society. Mark Mahowald. 1 January 1988. 103. 4. 1299–1304. 10.2307/2047129. free.
