Generators for the mod 2 cohomology of the Steinberg summand of Thom spectra over B(Z/2)n

JOURNAL OF ALGEBRA

卷:381

Article

Nguyen Dang Ho Hai

关键词: Steenrod algebra;    Hit problem;    Steinberg module;   

DOI  :  10.1016/j.jalgebra.2013.02.009

来源: Elsevier

【 摘 要 】

Let L-n,L-k be the Steinberg summand of the ideal generated by the k-th power of the top Dickson class of H*(B(Z/2)(n); Z/2). The module L-n,L-k is the mod 2 cohomology of the Steinberg summand of a Thom spectrum over the classifying space B(Z/2)(n). In this paper, using the Kameko map (Kameko, 1990 [6]) and short exact sequences induced by the cofibration sequences constructed by Takayasu (1999) [15], we construct a minimal generating set for L-n,L-k as a module over the mod 2 Steenrod algebra. This generalises the result of Masateru Inoue (2002) [5] for the cases k = 0, 1. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free