A questão Michael Atiyah é um assunto de grande importância que impacta a vida de milhões de pessoas em todo o mundo. Esta é uma questão complexa e multifacetada que abrange uma ampla gama de aspectos, desde o nível pessoal ao global. Neste artigo, exploraremos diferentes perspetivas e abordagens relacionadas com Michael Atiyah, analisando a sua relevância hoje e refletindo sobre as suas implicações a longo prazo. Através de uma análise detalhada e rigorosa, tentaremos esclarecer este tópico e proporcionar ao leitor uma compreensão mais profunda e completa de Michael Atiyah.
Michael Atiyah
Michael Francis Atiyah
Nascimento
Michael Francis Atiyah 22 de abril de 1929 Hampstead
Medalha Copley (In recognition of his fundamental contributions to a wide range of topics in geometry, topology, analysis and theoretical physics., 1988)
President's Medal (In recognition of his outstanding contributions to a broad range of topics in mathematics, many of which have provided highly significant foundations to the development of theoretical physics; and of his eminent leadership within the scientific community., 2008)
1955: Some Applications of Topological Methods in Algebraic Geometry
Obras destacadas
teorema do índice de Atiyah-Singer, algebroide de Atiyah, sequência espectral de Atiyah–Hirzebruch, Atiyah–Segal completion theorem, Atiyah–Hitchin–Singer theorem, teorema de ponto fixo de Atiyah–Bott, Atiyah–Bott formula, espaço de Atiyah–Hitchin, Atiyah-Jänich theorem, Atiyah conjecture on configurations, Atiyah–Jones conjecture, Atiyah conjecture
Esta subseção lista todos os livros escritos por Atiyah; omite alguns livros que ele editou.
Atiyah, Michael F.; Macdonald, Ian G. (1969), Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., MR0242802. A classic textbook covering standard commutative algebra.
Atiyah, Michael F. (1970), Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Cologne: Westdeutscher Verlag, MR0263102. Reprinted as (Atiyah 1988b, item 50).
Atiyah, Michael F. (1974), Elliptic operators and compact groups, Lecture Notes in Mathematics, Vol. 401, Berlin, New York: Springer-Verlag, MR0482866. Reprinted as (Atiyah 1988c, item 78).
Atiyah, Michael F. (1979), Geometry of Yang–Mills fields, Scuola Normale Superiore Pisa, Pisa, MR554924. Reprinted as (Atiyah 1988e, item 99).
Atiyah, Michael F. (1988a), Collected works. Vol. 1 Early papers: general papers, ISBN978-0-19-853275-0, Oxford Science Publications, The Clarendon Press Oxford University Press, MR951892.
Atiyah, Michael F. (1988b), Collected works. Vol. 2 K-theory, ISBN978-0-19-853276-7, Oxford Science Publications, The Clarendon Press Oxford University Press, MR951892.
Atiyah, Michael F. (1988c), Collected works. Vol. 3 Index theory: 1, ISBN978-0-19-853277-4, Oxford Science Publications, The Clarendon Press Oxford University Press, MR951892.
Atiyah, Michael F. (1988d), Collected works. Vol. 4 Index theory: 2, ISBN978-0-19-853278-1, Oxford Science Publications, The Clarendon Press Oxford University Press, MR951892.
Atiyah, Michael F. (1988e), Collected works. Vol. 5 Gauge theories, ISBN978-0-19-853279-8, Oxford Science Publications, The Clarendon Press Oxford University Press, MR951892.
Atiyah, Michael F. (2004), Collected works. Vol. 6, ISBN978-0-19-853099-2, Oxford Science Publications, The Clarendon Press Oxford University Press, MR2160826.
Atiyah, Michael F. (1976), «Elliptic operators, discrete groups and von Neumann algebras», Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974), Asterisque, 32–33, Soc. Math. France, Paris, pp. 43–72, MR0420729. Reprinted in (Atiyah 1988d, paper 89). Formulation of the Atiyah "Conjecture" on the rationality of the L2-Betti numbers.
Atiyah, Michael F.; Singer, Isadore M. (1963), «The Index of Elliptic Operators on Compact Manifolds», Bull. Amer. Math. Soc., 69 (3): 322–433, doi:10.1090/S0002-9904-1963-10957-X. An announcement of the index theorem. Reprinted in (Atiyah 1988c, paper 56).
Atiyah, Michael F.; Singer, Isadore M. (1968a), «The Index of Elliptic Operators I», Annals of Mathematics, 87 (3): 484–530, JSTOR1970715, doi:10.2307/1970715. This gives a proof using K theory instead of cohomology. Reprinted in (Atiyah 1988c, paper 64).
Atiyah, Michael F.; Segal, Graeme B. (1968), «The Index of Elliptic Operators: II», Annals of Mathematics, Second Series, 87 (3): 531–545, JSTOR1970716, doi:10.2307/1970716. This reformulates the result as a sort of Lefschetz fixed point theorem, using equivariant K theory. Reprinted in (Atiyah 1988c, paper 65).
Atiyah, Michael F.; Singer, Isadore M. (1968b), «The Index of Elliptic Operators III», Annals of Mathematics, Second Series, 87 (3): 546–604, JSTOR1970717, doi:10.2307/1970717. This paper shows how to convert from the K-theory version to a version using cohomology. Reprinted in (Atiyah 1988c, paper 66).
Atiyah, Michael F.; Singer, Isadore M. (1971), «The Index of Elliptic Operators IV», Annals of Mathematics, Second Series, 93 (1): 119–138, JSTOR1970756, doi:10.2307/1970756 This paper studies families of elliptic operators, where the index is now an element of the K-theory of the space parametrizing the family. Reprinted in (Atiyah 1988c, paper 67).
Atiyah, Michael F.; Singer, Isadore M. (1971), «The Index of Elliptic Operators V», Annals of Mathematics, Second Series, 93 (1): 139–149, JSTOR1970757, doi:10.2307/1970757. This studies families of real (rather than complex) elliptic operators, when one can sometimes squeeze out a little extra information. Reprinted in (Atiyah 1988c, paper 68).
Atiyah, Michael F.; Bott, Raoul (1966), «A Lefschetz Fixed Point Formula for Elliptic Differential Operators», Bull. Am. Math. Soc., 72 (2): 245–50, doi:10.1090/S0002-9904-1966-11483-0. This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex. Reprinted in (Atiyah 1988c, paper 61).
Atiyah, Michael F.; Bott, Raoul (1967), «A Lefschetz Fixed Point Formula for Elliptic Complexes: I», Annals of Mathematics, Second Series, 86 (2): 374–407, JSTOR1970694, doi:10.2307/1970694 (reprinted in (Atiyah 1988c, paper 61))and Atiyah, Michael F.; Bott, Raoul (1968), «A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications», Annals of Mathematics, Second Series, 88 (3): 451–491, JSTOR1970721, doi:10.2307/1970721. Reprinted in (Atiyah 1988c, paper 62). These give the proofs and some applications of the results announced in the previous paper.