nLab Michael Atiyah

Sir Michael Atiyah was a British-Lebanese mathematician, a Fields’ medalist, and Abel prize winner (with Isadore Singer). He was professor of mathematics at Edinburgh University.

Selected writings

Introducing topological K-theory:

Introducing cobordism cohomology theory MSO:

Introducing the Atiyah-Bott-Shapiro orientation MSpin\toKO and MSpinc\toKU:

Introducing the Atiyah-Bott fixed point theorem:

Introducing what came to be known as Karoubi K-theory:

On Bott periodicity:

On commutative algebra:

On the KO-theory of complex projective 3-space:

  • Michael Atiyah, E. Rees, Vector bundles on projective 3-space Invent. Math.35, 131–153 (1976) (pdf)

Introducing the ADHM construction for Yang-Mills instantons:

On quantum anomalies via index theory:

On moment maps, equivariant de Rham cohomology and equivariant localization:

On group characters and group cohomology of finite groups:

  • Michael Atiyah, Characters and cohomology of finite groups, Publications Mathématiques de l’IHÉS, Volume 9 (1961) , p. 23-64 (numdam)

On the Atiyah-Hirzebruch spectral sequence

On KR-theory

On equivariant K-theory and the Atiyah-Segal completion theorem:

On Yang-Mills instantons:

On Yang-Mills monopoles:

  • Michael Atiyah, Nigel Hitchin, J. T. Stuart and M. Tabor, Low-Energy Scattering of Non-Abelian Magnetic Monopoles, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 315, No. 1533, New Developments in the Theory and Application of Solitons (Aug. 13, 1985), pp. 459-469 (jstor:37546)

On the moduli spaces of Yang-Mills monopoles:

On knot theory and Chern-Simons theory:

On skyrmions from KK-reduction of instantons in D=5 Yang-Mills theory (hadron Kaluza-Klein theory):

and in a variant on hyperbolic space:

On the Clay Millennium Problems

On M-theory on G₂-manifolds:

Introducing the Atiyah-Sutcliffe conjecture:

On the Arnold-Kuiper-Massey theorem and its further generalization to the 13-sphere being an Sp(1)-quotient of the octonionic projective plane:

On twisted K-theory and twisted equivariant K-theory:

On Raoul Bott:

On The Unreasonable Effectiveness of Physics in the Mathematical Sciences:

On patterns in the characteristic classes (Chern classes) of complex surfaces, together with some speculations about an anlogy with atomic number of atomic nuclei (inspired by hadron Kaluza-Klein theory):

On twistors:

Selected quotes

The aim of theory really is, to a great extent, that of systematically organizing past experience in such a way that the next generation, our students and their students and so on, will be able to absorb the essential aspects in as painless a way as possible, and this is the only way in which you can go on cumulatively building up any kind of scientific activity without eventually coming to a dead end.

(M.F. Atiyah, “How research is carried out”, Bull. IMA., 10:232–234, 1974)

category: people

Last revised on July 18, 2024 at 11:15:57. See the history of this page for a list of all contributions to it.