2014/04/21 by Geoffrey Powell, Powell, Geoffrey
Mathematics · #19L41 #55S10 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:19L41 #msc:55S10
paper · pdf · doi:10.48550/arxiv.1404.5200
Revision - mathematical content essentially unchanged (39 pages)
arxiv created 2014/12/26 · arxiv updated 2014/12/30
A structure theorem for bounded-below modules over the subalgebra A(1) of the mod 2 Steenrod algebra generated by Sq1, Sq2 is proved; this is applied to prove a classification theorem for a family of indecomposable A(1)-modules. The action of the A(1)-Picard group on this family is described, as is the behaviour of duality. The cohomology of dual Brown-Gitler spectra is identified within this family and the relation with members of the A(1)-Picard group is made explicit. Similarly, the cohomology of truncated projective spaces is considered within this classification; this leads to a conceptual understanding of various results within the literature. In particular, a unified approach to Ext-groups relevant to Adams spectral sequence calculations is obtained, englobing earlier results of Davis (for truncated projective spaces) and recent work of Pearson (for Brown-Gitler spectra).