The real Brauer group of a finite CW-complex
HTML articles powered by AMS MathViewer
- by Elisabetta Strickland PDF
- Proc. Amer. Math. Soc. 75 (1979), 163-168 Request permission
Abstract:
In this paper a complete description in homological terms of the real Brauer group ${\text {Br}_R}(X)$ of a finite CW-complex X is obtained, in analogy with Jean Pierre Serre’s result on the complex Brauer group ${\text {Br}_C}(X)$ and the author’s one for the orthogonal case. Precisely it is shown that \[ {\text {Br}_R}(X) \cong {H^2}(X,{Z_2}) \oplus {H^0}(X,{Z_2}).\]References
-
A. Grothendieck, Dix exposès sur la cohomologie des schemas, North-Holland, Amsterdam, 1968.
- Elisabetta Strickland, On the orthogonal Brauer group, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 62 (1977), no. 3, 341–347 (English, with Italian summary). MR 497657 N. Bourbaki, Algèbre, Hermann, Paris, 1950-1958, Chapitres 4-6.
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112 D. Sullivan, Geometric topology, Lecture notes, M.I.T., Cambridge, Mass., June 1970.
- Dale Husemoller, Fibre bundles, McGraw-Hill Book Co., New York-London-Sydney, 1966. MR 0229247
- N. Bourbaki, Éléments de mathématique. 23. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre 8: Modules et anneaux semi-simples, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1261, Hermann, Paris, 1958 (French). MR 0098114
- Gorô Azumaya, On maximally central algebras, Nagoya Math. J. 2 (1951), 119–150. MR 40287
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 163-168
- MSC: Primary 55R10; Secondary 14F20, 16A39
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529234-1
- MathSciNet review: 529234