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Frank Adams may also refer to Frank Dawson Adams a Canadian geologist. Frank Dawson Adams ( September 17, 1859 &ndash December 26, 1942) was a Canadian Geologist.

John Frank Adams (November 5, 1930 – January 7, 1989) was a British mathematician, one of the founders of homotopy theory. Events 1499 - Publication of the Catholicon in Treguier ( Brittany) Year 1930 ( MCMXXX) was a Common year starting on Wednesday (link will display 1930 calendar of the Gregorian calendar. Events 1325 - Alfonso IV becomes King of Portugal. 1558 - France takes Calais, the last continental Year 1989 ( MCMLXXXIX) was a Common year starting on Sunday (link displays 1989 Gregorian calendar) The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located A mathematician is a person whose primary area of study and research is the field of Mathematics. In Topology, two continuous functions from one Topological space to another are called homotopic ( Greek homos = identical

Contents

Life

He was born in Woolwich, a suburb in south-east London. Woolwich (ˈwʊlɪtʃ or /ˈwʊlɪdʒ/ is a suburb in south-east London, England in the London Borough of Greenwich, on the south side of the River London ( ˈlʌndən is the capital and largest urban area in the United Kingdom. He began research as a student of Abram Besicovitch, but soon switched to algebraic topology. Abram Samoilovitch Besicovitch (Besikovitch (Абрам Самойлович Безикович (24 January 1891 &ndash 2 November 1970 was a Russian - Jewish Algebraic topology is a branch of Mathematics which uses tools from Abstract algebra to study Topological spaces The basic goal is to find algebraic He received his Ph. D. from the University of Cambridge in 1956. The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the His thesis, written under the direction of Shaun Wylie, was titled On spectral sequences and self-obstruction invariants. Shaun Wylie (born 17 January 1913) is a British Mathematician and former World War II codebreaker 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). The Fielden Chair of Pure Mathematics is an endowed professorial position in the School of Mathematics University of Manchester, England. The University of Manchester is a " red brick " civic University located in Manchester, England. The Lowndean chair of Astronomy and Geometry is one of the two major Professorships in Astronomy at Cambridge University, alongside the Plumian Professorship He was elected a Fellow of the Royal Society in 1964. The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660

His interests included mountaineering — he would demonstrate how to climb right round a table at parties — and the game of Go. “Alpinist” redirects here See also Alpinist (magazine Mountaineering is the Sport, Hobby or Profession of

He died in a car accident in Brampton, Cambridgeshire. Brampton &ndash in Huntingdonshire (now part of Cambridgeshire) England &ndash is a Village near Godmanchester south west He is buried in the Chapel of Trinity College, Cambridge. Trinity College is a constituent college of the University of Cambridge in Cambridge, England.

Work

In the 1950s, homotopy theory was at an early stage of development, and unsolved problems abounded. In Topology, two continuous functions from one Topological space to another are called homotopic ( Greek homos = identical 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. Henri Paul Cartan ( July 8, 1904 &ndash August 13, 2008) was a son of Élie Cartan, and was as his father was a distinguished In the area of Mathematics known as Homological algebra, especially in Algebraic topology and Group cohomology, a spectral sequence is a In Mathematics, stable homotopy theory is that part of Homotopy theory (and thus Algebraic topology) concerned with all structure and phenomena that remain In Mathematics, the Adams spectral sequence is a Spectral sequence introduced by Frank Adams, to provide a computational tool in Stable homotopy theory This begins with Ext groups calculated over the ring of cohomology operations, which is the Steenrod algebra in the classical case. In Mathematics, the Ext functors of Homological algebra are Derived functors of Hom functors They were first used in Algebraic topology In Mathematics, the cohomology operation concept became central to Algebraic topology, particularly Homotopy theory, from the 1950s onwards in the shape In Algebraic topology, a branch of Mathematics, the Steenrod algebra is a structure occurring in the theory of Cohomology operations It is an object of 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. In Mathematics, in particular in Algebraic topology, the Hopf invariant is a Homotopy invariant of certain maps between Spheres Motivation In In Mathematics, the cohomology operation concept became central to Algebraic topology, particularly Homotopy theory, from the 1950s onwards in the shape 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. In Mathematics, the Adams spectral sequence is a Spectral sequence introduced by Frank Adams, to provide a computational tool in Stable homotopy theory In Mathematics, homology theory is the Axiomatic study of the intuitive geometric idea of homology of cycles on Topological spaces It can be broadly

Adams was also a pioneer in the application of K-theory. In Mathematics, K-theory is a tool used in several disciplines He invented the Adams operations in K-theory, which are derived from the exterior powers; they are now also widely used in purely algebraic contexts. In Mathematics, an Adams operation ψ k is a Cohomology operation in Topological K-theory, or any allied Adams introduced them in a 1962 paper in order to solve the famous vector fields on spheres problem. In Mathematics, the discussion of vector fields on spheres was a classical problem of Differential topology, beginning with the Hairy ball theorem, and Subsequently he used them to investigate the Adams conjecture which is concerned (in one instance) with the image of the J-homomorphism in the stable homotopy groups of spheres. In Mathematics, the J -homomorphism is a mapping from the Homotopy groups of the Special orthogonal groups to the Homotopy groups of spheres In Mathematics, the J -homomorphism is a mapping from the Homotopy groups of the Special orthogonal groups to the Homotopy groups of spheres In the mathematical field of Algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other A later paper of Adams and Michael F. Atiyah uses the Adams operations to give an extremely elegant and much faster version of the above-mentioned Hopf invariant one result. Sir Michael Francis Atiyah, OM, FRS, FRSE (b April 22, 1929) is a British Mathematician, and one of the In Mathematics, in particular in Algebraic topology, the Hopf invariant is a Homotopy invariant of certain maps between Spheres Motivation In

In 1974 Adams became the first recipient of the Senior Whitehead Prize, awarded by the London Mathematical Society. Year 1974 ( MCMLXXIV) was a Common year starting on Tuesday (link will display full calendar of the 1974 Gregorian calendar. The Senior Whitehead Prize of the London Mathematical Society (LMS is currently awarded in odd numbered years in memory of John Henry Constantine Whitehead, president The London Mathematical Society ( LMS) is the leading mathematical society in England. [1]

Adams had many talented students, and was highly influential in the development of algebraic topology in Britain and worldwide.

Recognition

The main mathematics research seminar room in the Alan Turing Building at the University of Manchester is named in his honour. This article is about the Alan Turing Building in Manchester there is another building of the the same name at QinetiQ in Malvern The University of Manchester is a " red brick " civic University located in Manchester, England.

External links

References

  1. ^ London Mathematical Society. The MacTutor History of Mathematics archive is an award-winning website maintained by John J List of Prizewinners. Retrieved on 2007-07-08. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 939 - The Major Occultation or Ghaybat el-Kubra of Muhammad al-Mahdi 1099 - First Crusade: 15000


Preceded by
Max Newman		 Fielden Chair of Pure Mathematics Succeeded by
Ian G. Macdonald
Maxwell Herman Alexander Newman ( February 7 1897 &ndash February 22 1984) was a British Mathematician and Codebreaker The Fielden Chair of Pure Mathematics is an endowed professorial position in the School of Mathematics University of Manchester, England. Ian G Macdonald (born 1928 in London, England) is a British mathematician known for his contributions to Symmetric functions Special functions
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