From page 6 of these solutions:

the differential\begin{equation}d_2: H_p(X,\Omega_1^{Spin})\rightarrow H_{p-2}(X,\Omega_2^{Spin})\end{equation}connecting the 1-st and the 2-nd row is the $\textbf{dual}$ of second Steenrod cohomology operation $Sq^2$.

Can someone please explain to me why this is true?

  • $\begingroup$ Warmest welcome to MO $\endgroup$ – user21574 May 31 '14 at 11:44
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    $\begingroup$ I would imagine that this is for similar reasons as those given by Tyler Lawson here mathoverflow.net/questions/62642/… for why $d_3$ in the AHSS for complex K-theory is the integral $Sq^3$. $\endgroup$ – Mark Grant May 31 '14 at 13:22

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