nLab John Frank Adams (changes)
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John Frank Adams (1930-1989) was a British mathematician who made a great contribution to algebraic topology and in particular stable homotopy theory.
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Peter May, Reminiscences of the Life and Mathematics of J. Frank Adams (pdf)
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Ioan James, John Frank Adams (pdf, pdf)
Selected writings
On the cobar construction:
- John F. Adams: On the cobar construction, PNAS 42 7 (1956) 409-412 [[doi:10.1073/pnas.42.7.409](https://doi.org/10.1073/pnas.42.7.409)]
Introducing the Adams-Hilton model for the Pontrjagin ring-structure on the homology of a based loop space, refined to the singular chain complex:
- John F. Adams, Peter J. Hilton, On the chain algebra of a loop space, Commentarii Mathematici Helvetici 30 (1956) 305–330 [[doi:10.1007/BF02564350](https://doi.org/10.1007/BF02564350)]
Strengthening of the original Brown representability theorem:
- John Frank Adams: A variant of E. H. Brown’s representability theorem, Topology 10 (1971) 185–198 [doi:10.1016/0040-9383(71)90003-6]
On localization and completion in algebraic topology, via idempotent monads:
- John Frank Adams, Zbigniew Fiedorowicz, Localisation and Completion with an addendum on the use of Brown-Peterson homology in stable homotopy, based on 1973 lectures by Adams [[arXiv:1012.5020](https://arxiv.org/abs/1012.5020)]
On stable homotopy theory and generalized (Eilenberg-Steenrod) cohomology:
- John Frank Adams, Stable homotopy and generalized homology, Chicago Lectures in Mathematics, The University of Chicago Press (1974) [[ucp:bo21302708](https://www.press.uchicago.edu/ucp/books/book/chicago/S/bo21302708.html), pdf]
On the work of Henri Cartan in relation to homotopy theory:
- John Frank Adams, The work of M. H. Cartan in its relation with homotopy theory, Colloque analyse et topologie,Astérisque no. 32-33 (1976), p. 29-41 (numdam:AST_1976__32-33__29_0/)
On infinite loop spaces and $A_n$-spaces, $A_\infty$-algebras:
- John Adams, Infinite loop spaces, Hermann Weyl lectures at IAS, Annals of Mathematics Studies 90 Princeton University Press (1978) [[ISBN:9780691082066](https://press.princeton.edu/books/paperback/9780691082066/infinite-loop-spaces-am-90-volume-90), doi:10.1515/9781400821259]
On Lie groups:
- Frank Adams, Lectures on Lie groups, University of Chicago Press (1982) [[ISBN:9780226005300](https://press.uchicago.edu/ucp/books/book/chicago/L/bo3614673.html), gbooks]
Related entries
Last revised on September 19, 2026 at 10:32:08. See the history of this page for a list of all contributions to it.