John Frank Adams

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Frank Adams (right) with Dieter Doll in Aarhus in 1962

John Frank Adams , called Frank Adams (born November 5, 1930 in Woolwich , † January 7, 1989 in Brampton in Huntingdonshire ) was an English mathematician who was one of the leading algebraic topologists . In particular, he dealt with homotopy theory.

Live and act

After two years of service with the Royal Engineers, Adams studied from 1948 at Trinity College in Cambridge , where he worked under Besikowitsch in geometric dimension theory and later under Shaun Wylie on topology. The year 1954 set the trend for him, when he met the algebraic topologist JHC Whitehead as a junior lecturer in Oxford . In 1955 he received his doctorate in Cambridge with Shaun Wylie with a thesis on spectral sequences , which earned him the Fellowship of Trinity College. 1956 was followed by the introduction of the algebraic topology method, later called the " Adams spectral sequence ". During a stay in Chicago and Princeton in 1957/58 , he solved a classic problem of Heinz Hopf's topology using the number of mappings between spheres with Hopf invariant 1. After his return, he turned to K-theory as a lecturer at Cambridge , with which he proved a conjecture about the number of linearly independent vector fields on spheres (using his " Adams operations "). From 1962 he was a lecturer and from 1964 professor in Manchester ("Fielden Chair"). In 1970 he became the successor to William Hodge Professor ("Lowndean Professor of Astronomy and Geometry") in Cambridge.

Adams was accepted as a member (" Fellow ") in the Royal Society in London in 1964, which awarded him the New Year's Eve Medal in 1982 . In 1963 he received the Senior Berwick Prize of the London Mathematical Society and in 1974 was the first to receive their Senior Whitehead Prize . In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow (A Survey of Homotopy Theory) and in 1962 he was an Invited Speaker at the ICM in Stockholm ( Application of the Grothendieck-Atiyah-Hirzebruch functor K (X) ). In 1985 he became a member of the US National Academy of Sciences . He was also a member of the Royal Danish Academy of Sciences .

Adams died in a car accident just a few miles from his home. He had been married to a Congregationalist pastor since 1953 and had four children. His hobbies included mountaineering and the game of go . His brother was Vice Marshal of the Royal Air Force .

His PhD students include John Greenlees , Peter Johnstone , Andrew Ranicki .

Fonts

Books

  • Stable homotopy theory , 1964, Springer, Lecture Notes in Mathematics
  • Lectures on Lie groups , 1969
  • Algebraic topology: a student's guide , 1972 (with reprints)
  • Stable homotopy theory and generalized homology , 1974
  • Localization and completion , 1975
  • Infinite loop spaces , 1978
  • Lectures on exceptional Lie groups , 1996
  • May, Thomas (Ed.): Selected works of J. Frank Adams , 2 vols., Cambridge 1992

Publications (selection)

  • with Hilton : On the chain algebra of a loop space. Comment. Math. Helv. 30 (1956), 305-330.
  • On the non existence of elements of Hopf invariant one , Annals of Mathematics Vol. 72 (1960), 20-104.
  • Vector fields on spheres , Annals of Mathematics Vol. 75 (1962), pp. 603-632.
  • On the groups J (X). I. Topology 2: 181-195 (1963). II. Ibd. 3 (1963), 137-171. III. ibid. 3 (1965), 193-222. IV. Ibid. 5 (1966) 21-71.
  • with Atiyah : K-theory and the Hopf invariant. uart. J. Math. Oxford Ser. (2) 17: 31-38 (1966).
  • Maps between classifying spaces. I. (with Mahmud) Inv. Math. 35: 1-41 (1976). II. Ibd. 49 (1978), no. 1, 1-65.
  • with Wilkerson: Finite H-spaces and algebras over the Steenrod algebra. Ann. of Math. (2) 111 (1980) no. 1, 95-143

literature

  • IM James: Biographical memoirs of the fellows of the Royal Society , 1990 (and article in Dictionary of National Biography 2004 and Bulletin London Math. Society 1997 with CTCWall)
  • May: Reminiscences of the Life and Mathematics of John Frank Adams , Mathematical Intelligencer 1990
  • May: The work of Frank Adams , London Math. Society Lecture Notes Vol. 175, 1992, 1

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
personal data
SURNAME Adams, John Frank
BRIEF DESCRIPTION English mathematician
DATE OF BIRTH 5th November 1930
PLACE OF BIRTH Woolwich
DATE OF DEATH January 7, 1989
Place of death at Brampton