Brown–Gitler spectrum
From HandWiki
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]
- [math]\displaystyle{ \Sigma^n A/ \{ \operatorname{Sq}^i : 2i \gt n\} A \cong G(n). }[/math]
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]
References
- ↑ 1.0 1.1 "Brown–Gitler spectrum in nLab". https://ncatlab.org/nlab/show/Brown-Gitler%20spectrum.
- ↑ "Brown–Gitler Spectra". https://ncatlab.org/nlab/files/GoerssOnBrownGitler.pdf.
- ↑ Brown, Edgar H. Jr.; Gitler, Samuel (1973). "A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra". Topology 12 (3): 283–295. doi:10.1016/0040-9383(73)90014-1.
- ↑ 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. ISBN 9780821836767. https://books.google.com/books?id=EZYbCAAAQBAJ&dq=brown+gitler&pg=PA4.
- ↑ Cohen, Fred R.; Davis, Donald M.; Goerss, Paul G.; Mahowald, Mark E. (1 January 1988). "Integral Brown–Gitler Spectra". Proceedings of the American Mathematical Society 103 (4): 1299–1304. doi:10.2307/2047129.
External links
- Hazewinkel, Michiel, ed. (2001), "Brown-Gitler_spectra", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Brown-Gitler_spectra
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