Remark 9.4.17. Normalize the generator of \(H^2(\CP ^\infty ;\Q )\) by requiring that its restriction to \(\CP ^1\) is \(c_1(H)\), where \(H\) is the tautological line bundle of Definition 9.3.9. With this convention, the operation above agrees with the classical Chern character characterized on line bundles by \[ \mathrm {ch}(L)=e^{c_1(L)}. \] We do not develop the theory of Chern classes here; see Milnor and Stasheff (1974) and Hatcher (2003), Section 4.1.
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