Frank Adams may also refer to Frank Dawson Adams a Canadian geologist.

John Frank Adams (November 5, 1930 – January 7, 1989) was a British mathematician, one of the founders of homotopy theory.

He began research as a student of Besicovitch, but switched to algebraic topology. 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; the Steenrod algebra in the classical case. For an extraordinary cohomology theory there is the Adams-Novikov spectral sequence , a computational tool of great potential scope.

He was also a pioneer in the application of K-theory, solving the Hopf invariant one problem with its aid. The Adams operations in K-theory are derived from the exterior powers, and are now widely widely used in purely algebraic contexts. The Adams conjecture on the J-homomorphism is related to the homotopy groups of spheres.

He was born in Woolwich, London England, and died in a car accident near Cambridge, England. He became Lowndean Professor at the University of Cambridge. His interests included mountaineering — he would demonstrate how to climb right round a table at parties — and go.

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