In K-theory we have the Todd class and the $\hat A$ class.


The Todd class is named after the Cambridge geometer John Arthur Todd.


Where does the name $\hat A$ come from? Does the A stand for Atiyah?



Where does the $\hat A$ class get its name?
It seems that the $\hat{A}$ genus was first introduced in Section 23 of the paper "Characteristic Classes and Homogeneous Spaces, II", by Borel and Hirzebruch (1959). It is presented as a small modification of some $A$-genus previously introduced by Hirzebruch in his book "Neue Topologische Methoden in der Algebraischen Geometrie" (1956) (the $A$-genus is the genus associated to the power series $2z^{1/2}/sh(2z^{1/2})$, whereas the $\hat{A}$-genus is associated to the power series $(z^{1/2}/2)/sh(z^{1/2}/2)$). It is a resonable explanation of the hat on $\hat{A}$: first some $A$-genus was introduced, then some small modification $\hat{A}$, and it was only gradually realized that the $\hat{A}$-genus was more important that the $A$-genus (to the point that today I don't know if anyone still uses the terminology $A$-genus). It seems unclear if there is a good explanation for the $A$ in $A$-genus except that $A$ is a quite common letter. When Hirzebruch used the letter $A$ in his book published in 1956, I don't think that Atiyah was already thinking about these questions and so it seems very unlikely that $A$ stand for Atiyah.


