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Relations Between Kernels and Images of Reduced Powers for Some Right 𝒜 p -Modules

Theodore Popelensky

Moscow State Lomonosov University, Department of Mechanics and Mathematics, Moscow, Russia

Abstract: We investigate the right action of the mod p Steenrod algebra 𝒜 p on the homology H * (L s , p ) where L=B 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 β and the intersection of images of P p i+1 -1 and of β. Namely one can check that i=0 k imP p i+1 -1 i=0 k kerP p i and i=0 k imP p i+1 -1 imβ i=0 k kerP p i kerβ. 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

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Electronic fulltext finalized on: 26 Apr 2018. This page was last modified: 11 Mai 2018.

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