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May 2011 Realizing a complex of unstable modules
Hai Nguyen Dang Ho, Lionel Schwartz
Proc. Japan Acad. Ser. A Math. Sci. 87(5): 83-87 (May 2011). DOI: 10.3792/pjaa.87.83

Abstract

In a preceding article~[7] the authors and Tran Ngoc Nam constructed a minimal injective resolution of the mod 2 cohomology of a Thom spectrum. A Segal conjecture type theorem for this spectrum was proved. In this paper one shows that the above mentioned resolutions can be realized topologically. In fact there exists a family of cofibrations inducing short exact sequences in mod 2 cohomology. The resolutions above are obtained by splicing together these short exact sequences. Thus the injective resolutions are realizable in the best possible sense. In fact our construction appears to be in some sense an injective closure of one of Takayasu. It strongly suggests that one can construct geometrically (not only homotopically) certain dual Brown-Gitler spectra.

Citation

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Hai Nguyen Dang Ho. Lionel Schwartz. "Realizing a complex of unstable modules." Proc. Japan Acad. Ser. A Math. Sci. 87 (5) 83 - 87, May 2011. https://doi.org/10.3792/pjaa.87.83

Information

Published: May 2011
First available in Project Euclid: 26 April 2011

zbMATH: 1234.55012
MathSciNet: MR2803896
Digital Object Identifier: 10.3792/pjaa.87.83

Subjects:
Primary: 55S10 , 55T15
Secondary: 55P42

Keywords: Adams spectral sequence , Brown-Gitler spectrum , unstable module

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 5 • May 2011
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