Minc's generating function and a Segal conjecture for Thom spectra. La fonction generatrice de Minc et une conjecture de Segal pour certains spectres de Thom

Dang Ho Hai Nguyen; Lionel Schwartz; Ngoc Nam Tran

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arXiv · 0907.3698

Minc's generating function and a Segal conjecture for Thom spectra. La fonction generatrice de Minc et une conjecture de Segal pour certains spectres de Thom

Dang Ho Hai Nguyen·Lionel Schwartz·Ngoc Nam Tran

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Abstract

One constructs minimal injective resolutions for certain unstable modules that appears to be the mod 2 cohomology of Thom spectra. The terms of the resolution are tensor products of Brown-Gitler modules and Steinberg modules introduced by S. Mitchell and S. Priddy. A combinatorial result of Andrews shows that the alternating sum of the Poincare series of the considered modules is zero. One gives homotopical applications of this result.

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Dang Ho Hai Nguyen, Lionel Schwartz, Ngoc Nam Tran. 2009-07-21. Minc's generating function and a Segal conjecture for Thom spectra. La fonction generatrice de Minc et une conjecture de Segal pour certains spectres de Thom. https://arxiv.org/abs/0907.3698

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