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]

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. ^ a b "Brown–Gitler spectrum in nLab".
  2. ^ "Brown–Gitler Spectra" (PDF).
  3. ^ 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. MR 0391071.
  4. ^ 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 – via Google Books.
  5. ^ 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. JSTOR 2047129.