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]
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
- Hazewinkel, Michiel, ed. (2001) [1994], "Brown-Gitler_spectra", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
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