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.
Memories of Sir Michael Atiyah, Notices of the AMS [pdf, pdf]
Bernd Schroers, Michael Atiyah and Physics: the Later Years [arXiv:1910.10630]
Alain Connes, Joseph Kouneiher: Sir Michael Atiyah, a Knight Mathematician A tribute to Michael Atiyah, an inspiration and a friend (arxiv:1910.07851)
Nigel Hitchin, Sir Michael Atiyah OM. 22 April 1929–11 January 2019, Biographical Memoirs of the FRS, September 2020 (doi:10.1098/rsbm.2020.0001)
Nigel Hitchin, Michael Atiyah: Geometry and Physics, 2020 (pdf, pdf)
Introducing topological K-theory:
M. F. Atiyah, F. Hirzebruch, Riemann-Roch theorems for differentiable manifolds, Bull. Amer. Math Soc. vol. 65 (1959) pp. 276-281 (euclid:bams/1183523205)
M. F. Atiyah, F. Hirzebruch, Vector bundles and homogeneous spaces, 1961, Proc. Sympos. Pure Math., Vol. III pp. 7–38 American Mathematical Society, Providence, R.I. (doi:10.1142/9789814401319_0008, web, MR 0139181)
Michael Atiyah, K-theory, Harvard Lecture 1964 (notes by D. W. Anderson), Benjamin 1967 (pdf, pdf)
Introducing cobordism cohomology theory MSO:
Introducing the Atiyah-Bott-Shapiro orientation MSpinKO and MSpincKU:
Introducing the Atiyah-Bott fixed point theorem:
Michael F. Atiyah, Raoul Bott: A Lefschetz fixed point formula for elliptic differential operators, Bull. Amer. Math. Soc. 72 (1966) 245-250 [doi:10.1090/S0002-9904-1966-11483-0, pdf]
Michael F. Atiyah, Raoul Bott: A Lefschetz Fixed Point Formula for Elliptic Complexes: I, Annals of Mathematics 86 2 (1967) 374-407 [doi:10.2307/1970694, jstor:1970694]
Introducing what came to be known as Karoubi K-theory:
On Bott periodicity:
Concerning spin structures on Riemann surfaces:
On the KO-theory of complex projective 3-space:
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:
On the Atiyah-Hirzebruch spectral sequence
On KR-theory
On equivariant K-theory and the Atiyah-Segal completion theorem:
Michael Atiyah, John David Stuart Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. Volume 61, Number 2 (1978), 97-118 (arXiv:1103904210)
Michael Atiyah, Instantons in two and four dimensions, Commun. Math. Phys. 93, 437–451 (1984) (doi:10.1007/BF01212288)
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
Introducing the Atiyah-Sutcliffe conjecture:
Michael F. Atiyah, Paul M. Sutcliffe, The geometry of point particles, Proc. Roy. Soc. London Ser. A 458 (2002), 1089–1115 (hep-th/0105179, doi:10.1098/rspa.2001.0913)
Michael Atiyah, Joseph Malkoun, The Relativistic Geometry and Dynamics of Electrons, Found Phys 48, 199–208 (2018) (doi:10.1007/s10701-018-0139-2)
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:
(beware of the false claim in AS04 p 39 that in the compact open topology is not a topological group, corrected by Schottenloher 2013, Espinoza & Uribe 2014, going back to Schottenloher 1995)
On physics and mathematics (quantum mechanics, string theory, …, cf. at The Unreasonable Effectiveness…):
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):
Michael Atiyah, Nicholas Manton, Bernd Schroers, Geometric Models of Matter, Proceedings of the Royal Society A (arXiv:1108.5151, doi:10.1098/rspa.2011.0616)
Michael Atiyah, Nicholas Manton, Complex Geometry of Nuclei and Atoms, International Journal of Modern Physics AVol. 33, No. 24, 1830022 (2018) (arXiv:1609.02816, doi:10.1142/S0217751X18300223)
Michael Atiyah, Geometric Models of Helium, Modern Physics Letters AVol. 32, No. 14, 1750079 (2017) (arXiv:1703.02532, doi:10.1142/S0217732317500791)
On twistors:
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)
twisted K-theory, equivariant K-theory, twisted equivariant K-theory
…many more…
Last revised on June 22, 2025 at 17:16:55. See the history of this page for a list of all contributions to it.