Proceedings of the Japan Academy, Series A, Mathematical Sciences

Realizing a complex of unstable modules

Hai Nguyen Dang Ho and Lionel Schwartz

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 5 (2011), 83-87.

First available in Project Euclid: 26 April 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55S10: Steenrod algebra 55T15: Adams spectral sequences
Secondary: 55P42: Stable homotopy theory, spectra

Unstable module Brown-Gitler spectrum Adams spectral sequence


Nguyen Dang Ho, Hai; Schwartz, Lionel. Realizing a complex of unstable modules. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 5, 83--87. doi:10.3792/pjaa.87.83.

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