Frank Adams

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

Life and work

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

Adams was taken in 1964 as a member ( "Fellow" ) to the Royal Society in London, the 1982 Sylvester Medal awarded him. In 1963 he was awarded the Senior Berwick Prize of the London Mathematical Society in 1974 and the first winner of the 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 invited speaker at the ICM in Stockholm (application of the Atiyah - Hirzebruch - Grothendieck functor K (X)). In 1985 he became a member of the National Academy of Sciences of the United States. He was also a member of the Royal Danish Academy of Sciences.

Adams died in a car accident just a few kilometers from his home. He was married to a pastor of the Congregational 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 doctoral include John Greenlees, Peter Johnstone, Andrew Ranicki.

Writings

  • 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
  • Localisation 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), S.603 - 632.
  • Groups on the Y ( X). I. Topology 2 (1963 ), 181-195. II ibid., 3 (1963 ), 137-171. III. ibid 3 (1965 ), 193-222. IV ibid., 5 (1966 ) 21-71.
  • Invariant.uart K -theory and the Hopf: with Atiyah. J. Math Oxford Ser. (2 ) 17 ( 1966), 31-38.
  • Maps in between classifying spaces. I. ( Mahmoud ) Inv. Math 35 (1976 ), 1-41. II ibid 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
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