Dyer-Lashof Ops giving Steenrod Ops in Ext?

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Mike Hill

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Aug 25, 2005, 2:05:06 PM8/25/05
to Algebraic Topology
I have a quick question for the people on this list who know more about
this stuff than I. I've started computing Ext_{A(2)}(F_3,F_3) using a
May spectral sequence. My question stems from the following
differentials:

d(v_1)=v_0 a_1 &
d(v_2)=v_1 a_2,

where v_i is [\tau_i] in the bar complex (appropriately filtered), and
a_i=[\xi_1^{3^i}]. Now the a_i are related as

P^0(a_i)=a_{i+1}. The \tau_i are related by Dyer-Lashof ops, I think
called Q_{p^i} (or maybe Q^i, I never remember). My question is how the
Steenrod action in Ext reflects the Dyer-Lashof operation action in
A_*. This observation makes me think that there is some kind of
relation, but I'm not sure what it could be.

Thanks,
Mike

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