Frank Adams
| Frank Adams | |
|---|---|
Frank Adams (right) with Dieter Puppe in 1962 in Aarhus
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| Born |
5 November 1930 Woolwich |
| Died | 7 January 1989 (aged 58) |
| Nationality | British |
| Fields | Mathematics |
| Institutions | University of Cambridge |
| Alma mater | University of Cambridge |
| Doctoral advisor | Shaun Wylie |
| Doctoral students |
Béla Bollobás Peter Johnstone Andrew Ranicki Nigel Ray C. T. C. Wall |
| Notable awards |
Berwick Prize (1963) Senior Whitehead Prize (1974) Sylvester Medal (1982) |
John Frank Adams FRS (5 November 1930 – 7 January 1989) was a British mathematician, one of the founders of homotopy theory.
He was born in Woolwich, a suburb in south-east London, and attended Bedford School. He began research as a student of Abram Besicovitch, but soon switched to algebraic topology. He received his PhD from the University of Cambridge in 1956. His thesis, written under the direction of Shaun Wylie, was titled On spectral sequences and self-obstruction invariants. He held the Fielden Chair at the University of Manchester (1964–1970), and became Lowndean Professor of Astronomy and Geometry at the University of Cambridge (1970–1989). He was elected a Fellow of the Royal Society in 1964.
His interests included mountaineering—he would demonstrate how to climb right round a table at parties (a Whitney traverse)—and the game of Go.
He died in a car accident in Brampton, Cambridgeshire. There is a memorial plaque for him in the Chapel of Trinity College, Cambridge.
In the 1950s, homotopy theory was at an early stage of development, and unsolved problems abounded. Adams made a number of important theoretical advances in algebraic topology, but his innovations were always motivated by specific problems. Influenced by the French school of Henri Cartan and Jean-Pierre Serre, he reformulated and strengthened their method of killing homotopy groups in spectral sequence terms, creating the basic tool of stable homotopy theory now known as the Adams spectral sequence. This begins with Ext groups calculated over the ring of cohomology operations, which is the Steenrod algebra in the classical case. He used this spectral sequence to attack the celebrated Hopf invariant one problem, which he completely solved in a 1960 paper by making a deep analysis of secondary cohomology operations. The Adams–Novikov spectral sequence is an analogue of the Adams spectral sequence using an extraordinary cohomology theory in place of classical cohomology: it is a computational tool of great potential scope.
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