Relations between kernels and images of reduced powers for some right Ap-modules
We investigate the right action of the mod p Steenrod algebra Ap on the homology H*(L^s,Zp) where L=BZp is the lens space. Following ideas of Ault and Singer we investigate the relation between intersection of kernels of the reduced powers Ppi and Bockstein element ? and the intersection of images of Ppi+1?1 and of ?. Namely one can check that ?ki=0 imPpi+1?1 ? ?ki=0 ker Ppi and ?ki=0 imPpi+1?1 ? im? ? ?k i=0 ker Ppi ? ker ?. We generalize Ault?s homotopy systems to p > 2 and examine when the reverse inclusions are true.
Keyword(s):
2021 ◽
Keyword(s):
2019 ◽
Vol 1
(1)
◽
pp. 15
Keyword(s):
Keyword(s):
2020 ◽
pp. 462-473