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By J. L. Dupont, I. H. Madsen

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15. Appendix to a paper of E. R. Reifenberg, Acta Math. 104 (1960), 76-91. Bibliography of J. F. Adams 23 16. The sphere, considered as an H-space mod p, Quart. J. Math. Oxford Ser. (2), 12 (1961), 52-60. 17. A finiteness theorem in homological algebra, Proc. Cambridge Philos. Soc. 57 (1961), 31-36. 18. On Chern characters and the structure of the unitary group, Proc. Cambridge Philos. Soc. 57 (1961), 189-199. 19. On formulae of Thom and Wu, Proc. London Math. Soc. (3) 11 (1961), 741-752. 20. Vector fields on spheres, Topology 1 (1962), 63-65.

If chr is the rth component of the Chern character, then chq,r(C) rationalizes to m(r)chq+r(C), and the relate appropriately to Steenrod operations when reduced mod p. Yuli Rudjak noted that some of the ideas Adams introduced here are relevant to the study of the orientability of various kinds of bundles. 3. Chern characters revisited (1971) [47] This gives a more modern and sophisticated approach to the Chern character. The image of H*(bu; Z) in H*(bu; Q) = Q[u], degu = 2, is shown to be the subgroup generated by {ur/m(r) I r > 0}.

QX of a topological space X. Furthermore, since Adams-Hilton models can be constructed to be relatively "small", they are quite useful for computational purposes. Explicit Adams-Hilton models are also reasonably easy to construct. If X is a simply-connected CW complex with a fixed cellular decomposition, then A (X) can be chosen to have generators corresponding to the cells in the decomposition and a differential encoding their attaching maps. While much is known about how Adams-Hilton models can be computed in general, until recently the relationships among the Adams-Hilton models for the fiber, base space and total space of a fibration had not been thoroughly investigated.

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