Publications de l’Institut Mathématique, Nouvelle Série Vol. 103[117] 
Relations Between Kernels and Images of Reduced Powers for Some Right ${\mathcal{A}}_{p}$ModulesTheodore PopelenskyMoscow State Lomonosov University, Department of Mechanics and Mathematics, Moscow, RussiaAbstract: We investigate the right action of the mod $p$ Steenrod algebra ${\mathcal{A}}_{p}$ on the homology ${H}_{*}({L}^{\wedge s},{\mathbb{Z}}_{p})$ where $L=B{\mathbb{Z}}_{p}$ is the lens space. Following ideas of Ault and Singer we investigate the relation between intersection of kernels of the reduced powers ${P}^{{p}^{i}}$ and Bockstein element $\beta $ and the intersection of images of ${P}^{{p}^{i+1}1}$ and of $\beta $. Namely one can check that ${\bigcap}_{i=0}^{k}im{P}^{{p}^{i+1}1}\subset {\bigcap}_{i=0}^{k}ker{P}^{{p}^{i}}$ and ${\bigcap}_{i=0}^{k}im{P}^{{p}^{i+1}1}\cap \phantom{\rule{0.166667em}{0ex}}im\beta \subset {\bigcap}_{i=0}^{k}ker{P}^{{p}^{i}}\cap \phantom{\rule{0.166667em}{0ex}}ker\beta $. We generalize Ault’s homotopy systems to $p>2$ and examine when the reverse inclusions are true. Keywords: Steenrod algebra, reduced powers Classification (MSC2000): 55S10; 55R40; 57T25 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.
© 2018 Mathematical Institute of the Serbian Academy of Science and Arts
