Brown–Gitler spectrum
In topology, a discipline within mathematics, 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]
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 Segal conjecture and Burnside ring.[4]
Applications
Brown–Gitler spectra have had many important applications in homotopy theory.[5]
gollark: I'd assume that to actually operate on a large chunk of RAM you'd want to do something else.
gollark: *Apparently* this is just the script for my Discord bot. Boring.
gollark: I clicked "MEM" in `htop`.
gollark: I'm not joking about the mysterious Python program. I forgot what this actually is.
gollark: This makes it the most RAM-consuming thing on my server, followed by VictoriaMetrics, Factorio, systemd-journald, syncthing, and a mysterious python program.
References
- "Brown–Gitler spectrum in nLab".
- "Brown–Gitler Spectra" (PDF).
- Brown, Edgar H., Jr.; Gitler, Samuel (1973). "A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra". Topology. 12: 283–295. doi:10.1016/0040-9383(73)90014-1. MR 0391071.
- Gitler, Samuel; González, Jesús (1 January 2006). "Recent Developments in Algebraic Topology: A Conference to Celebrate Sam Gitler's 70th Birthday, December 3–6, 2003, San Miguel de Allende, México". American Mathematical Society – via Google Books.
- Cohen, Fred R.; Davis, Donald M.; Goerss, Paul G.; Mahowald, Mark E. (1 January 1988). "Integral Brown–Gitler Spectra". 103 (4): 1299–1304. doi:10.2307/2047129. JSTOR 2047129. Cite journal requires
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External links
- "Brown-Gitler_spectra", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
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