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Michael Atiyah - List of publications #


  • Atiyah, Michael F.; Macdonald, Ian G. (1969), Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., MR 0242802. 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, MR 0263102. 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, MR 0482866. Reprinted as (Atiyah 1988c, item 78).
  • Atiyah, Michael F. (1979), Geometry of Yang–Mills fields, Scuola Normale Superiore Pisa, Pisa, MR 554924. Reprinted as (Atiyah 1988e, item 99).
  • Atiyah, Michael F.; Hitchin, Nigel (1988), The geometry and dynamics of magnetic monopoles, M. B. Porter Lectures, Princeton University Press, ISBN 978-0-691-08480-0, MR 934202. Reprinted as (Atiyah 2004, item 126).
  • Atiyah, Michael F. (1988a), Collected works. Vol. 1 Early papers: general papers, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853275-0, MR 951892.
  • Atiyah, Michael F. (1988b), Collected works. Vol. 2 K-theory, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853276-7, MR 951892.
  • Atiyah, Michael F. (1988c), Collected works. Vol. 3 Index theory: 1, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853277-4, MR 951892.
  • Atiyah, Michael F. (1988d), Collected works. Vol. 4 Index theory:2, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853278-1, MR 951892.
  • Atiyah, Michael F. (1988e), Collected works. Vol. 5 Gauge theories, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853279-8, MR 951892.
  • Atiyah, Michael F. (1989), K-theory, Advanced Book Classics (2nd ed.), Addison-Wesley, ISBN 978-0-201-09394-0, MR 1043170. First edition (1967) reprinted as (Atiyah 1988b, item 45).
  • Atiyah, Michael F. (1990), The geometry and physics of knots, Lezioni Lincee. Lincei Lectures, Cambridge University Press, ISBN 978-0-521-39521-2, MR 1078014. Reprinted as (Atiyah 2004, item 136).
  • Atiyah, Michael F.; Iagolnitzer, Daniel (1997), Fields Medallists' Lectures, World Scientific, pp. 113–4, ISBN 981-02-3117-2.
  • Atiyah, Michael F. (2004), Collected works. Vol. 6, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853099-2, MR 2160826.
  • Atiyah, Michael F. (2007), Siamo tutti matematici (Italian: We are all mathematicians), Roma: Di Renzo Editore, p. 96, ISBN 88-8323-157-0.
  • Atiyah, Michael F. (1961), "Characters and cohomology of finite groups", Inst. Hautes Études Sci. Publ. Math. 9: 23–64, doi:10.1007/BF02698718. Reprinted in (Atiyah 1988b, paper 29).
  • Atiyah, Michael F.; Hirzebruch, Friedrich (1961), "Vector bundles and homogeneous spaces", Proc. Sympos. Pure Math. AMS 3: 7–38. Reprinted in (Atiyah 1988b, paper 28).
  • Atiyah, Michael F.; Segal, Graeme B. (1969), "Equivariant K-Theory and Completion", Journal of Differential Geometry 3: 1–18. Reprinted in (Atiyah 1988b, paper 49).
  • 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, MR 0420729. 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: 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", Ann. Math. (The Annals of Mathematics, Vol. 87, No. 3) 87 (3): 484–530, doi:10.2307/1970715, JSTOR 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 (The Annals of Mathematics, Vol. 87, No. 3) 87 (3): 531–545, doi:10.2307/1970716, JSTOR 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, doi:10.2307/1970717, JSTOR 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", The Annals of Mathematics 2nd Ser. (The Annals of Mathematics, Vol. 93, No. 1) 93 (1): 119–138, doi:10.2307/1970756, JSTOR 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 (The Annals of Mathematics, Vol. 93, No. 1) 93 (1): 139–149, doi:10.2307/1970757, JSTOR 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 (The Annals of Mathematics, Vol. 86, No. 2) 86 (2): 374–407, doi:10.2307/1970694, JSTOR 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 (The Annals of Mathematics, Vol. 88, No. 3) 88 (3): 451–491, doi:10.2307/1970721, JSTOR 1970721. Reprinted in (Atiyah 1988c, paper 62). These give the proofs and some applications of the results announced in the previous paper.
  • Atiyah, Michael F.; Bott, Raoul; Patodi, Vijay K. (1973), "On the heat equation and the index theorem", Invent. Math. 19 (4): 279–330, Bibcode 1973InMat..19..279A, doi:10.1007/BF01425417, MR 0650828; Atiyah, Michael F.; Bott, R.; Patodi, V. K. (1975), "Errata", Invent. Math. 28 (3): 277–280, Bibcode 1975InMat..28..277A, doi:10.1007/BF01425562, MR 0650829 Reprinted in (Atiyah 1988d, paper 79, 79a).
  • Atiyah, Michael F.; Schmid, Wilfried (1977), "A geometric construction of the discrete series for semisimple Lie groups", Invent. Math. 42: 1–62, Bibcode 1977InMat..42....1A, doi:10.1007/BF01389783, MR 0463358; Atiyah, Michael F.; Schmid, Wilfried (1979), "Erratum", Invent. Math. 54 (2): 189–192, Bibcode 1979InMat..54..189A, doi:10.1007/BF01408936, MR 0550183. Reprinted in (Atiyah 1988d, paper 90).
  • Atiyah, Michael (2010), Edinburgh Lectures on Geometry, Analysis and Physics


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