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.{{cite web|url=https://ncatlab.org/nlab/show/Brown-Gitler%20spectrum|title=Brown–Gitler spectrum in nLab}}
Brown–Gitler spectra are defined by the isomorphism:{{cite web|url=https://ncatlab.org/nlab/files/GoerssOnBrownGitler.pdf|title=Brown–Gitler Spectra}}
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History
The concept was introduced by mathematicians Edgar H. Brown and Samuel Gitler in a 1973 paper.{{cite journal|first1= Edgar H. Jr. | last1=Brown| author1-link=Edgar H. Brown| first2=Samuel| last2=Gitler|author-link2=Samuel Gitler Hammer | title=A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra|journal=Topology |volume= 12 |year=1973| issue=3|pages=283–295|mr=0391071|doi=10.1016/0040-9383(73)90014-1}}
In topology, Brown–Gitler spectrum is related to the concepts of the Segal conjecture
(proven in 1984) and the Burnside ring.{{cite book|url=https://books.google.com/books?id=EZYbCAAAQBAJ&dq=brown+gitler&pg=PA4|title=Recent Developments in Algebraic Topology: A Conference to Celebrate Sam Gitler's 70th Birthday, December 3–6, 2003, San Miguel de Allende, México|first1=Samuel|last1=Gitler|author-link1=Samuel Gitler Hammer | first2=Jesús|last2=González|date=1 January 2006|publisher=American Mathematical Society|isbn=9780821836767|via=Google Books}}
Applications
Brown–Gitler spectra have had many important applications in homotopy theory.{{cite journal|jstor=2047129|title=Integral Brown–Gitler Spectra|first1=Fred R.|last1=Cohen|first2=Donald M.|last2=Davis|first3=Paul G.|last3=Goerss|first4=Mark E.|last4=Mahowald|journal=Proceedings of the American Mathematical Society|author-link4=Mark Mahowald| date=1 January 1988|volume=103|issue=4|pages=1299–1304|doi=10.2307/2047129|doi-access=free}}
References
{{Reflist}}
External links
- {{eom|id=Brown-Gitler_spectra|title=Brown-Gitler_spectra}}
{{DEFAULTSORT:Brown-Gitler spectrum}}