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:

On Bott periodicity:

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

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:

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:

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 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 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