Andrew Casson

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Andrew J. Casson (* 1943 ) is a British mathematician who studies geometric topology .

Andrew Casson (1991)

Life

Casson studied at the University of Liverpool with CTC Wall and then went to the University of Cambridge , where he became a Fellow of Trinity College . He was then a professor in Cambridge, 1981 to 1986 at the University of Texas at Austin , 1986 to 1999 at the University of California, Berkeley and since 2000 at Yale University , where he was chairman of the mathematics department from 2004 to 2007.

Around 1967 he and Dennis Sullivan refuted the “ main conjecture ” about the unambiguous triangulability of topological manifolds (established by Ernst Steinitz and Heinrich Tietze , 1908), which asserted the unambiguous triangulability of triangulable topological manifolds. They found an obstruction in higher (five and more) dimensions ( John Milnor found the first counterexamples in dimension 8 in 1961). In contrast, it is correct for up to three dimensions (Edward Brown 1963). Casson's work was originally supposed to be his dissertation at Wall in Liverpool, but he then submitted it as a qualification for the Fellowship of Trinity College (he never formally received a doctorate).

The integer Casson invariant for 3-manifolds and the Casson handles in the theory of topological 4-manifolds are named after him. Casson handles are certain 2-handles in 4 dimensions, they were used by Michael Freedman in his fundamental work on the classification of simply connected topological 4-manifolds from 1982 and the name comes from him.

Independent of David Gabai, he and Douglas Jungreis set the keystone for the proof of the Seifert fiber space conjecture , building on the work of Geoffrey Mess (his former doctoral student), Pekka Tukia and others.

Casson is a Fellow of the Royal Society . In 1991 he received the Oswald Veblen Prize . In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (A survey of recent developments in 3-dimensional topology) and in 1978 in Helsinki (Knot cobordism).

Fonts

Web links

Individual evidence

  1. ^ Casson, Jungreis, Convergence groups and Seifert fibered 3-manifolds, Invent. Math., Vol. 118, 1994, pp. 441-456.
personal data
SURNAME Casson, Andrew
ALTERNATIVE NAMES Casson, Andrew J.
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH 1943