Editing Michael Atiyah (section)

===Selected papers===
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*{{Citation|last=Atiyah|first=Michael F.|author-link=<!--Michael Atiyah-->|year=1961|title=Characters and cohomology of finite groups|journal=Inst. Hautes Études Sci. Publ. Math.|volume=9|issue=1 |pages=23–64|url=http://www.numdam.org/item?id=PMIHES_1961__9__23_0|doi=10.1007/BF02698718|s2cid=54764252}}. Reprinted in {{harv|Atiyah|1988b|loc=paper 29}}.
*{{cite book | editor-last=Allendorfer| editor-first=Carl B. |last1=Atiyah|first1=Michael F.|author-link1=Michael Atiyah|last2=Hirzebruch|first2=Friedrich|author-link2=Friedrich Hirzebruch|year=1961|title=Differential Geometry|volume=3| chapter=Vector bundles and homogeneous spaces|pages=7–38|doi=10.1090/pspum/003/0139181  | publisher=American Mathematical Society | publication-place=Providence |series=Proceedings of Symposia in Pure Mathematics|isbn=978-0-8218-1403-1}}. Reprinted in {{harv|Atiyah|1988b|loc=paper 28}}.
*{{Citation|last1=Atiyah|first1=Michael F.|author-link1=<!--Michael Atiyah-->|last2=Segal|first2=Graeme B.|author-link2=Graeme Segal|year=1969|title=Equivariant K-Theory and Completion|journal=Journal of Differential Geometry|volume=3|issue=1–2|pages = 1–18|doi=10.4310/jdg/1214428815|doi-access=free}}. Reprinted in {{harv|Atiyah|1988b|loc=paper 49}}.
*{{Citation|mr=0420729|last=Atiyah|first= Michael F.
|chapter=Elliptic operators, discrete groups and von Neumann algebras|title= Colloque "Analyse et Topologie" en l'Honneur de Henri Cartan (Orsay, 1974)|pages= 43–72|series= Asterisque|volume= 32–33|publisher= Soc. Math. France, Paris|year= 1976}}. Reprinted in {{harv|Atiyah|1988d|loc=paper 89}}. Formulation of the [[Atiyah conjecture|Atiyah "Conjecture"]] on the rationality of the L<sup>2</sup>-Betti numbers.
*{{Citation|last1= Atiyah|first1= Michael F. |last2=Singer|first2= Isadore M. |title=The Index of Elliptic Operators on Compact Manifolds|journal= Bull. Amer. Math. Soc.|volume= 69|issue= 3 |pages= 322–433|year= 1963 | doi = 10.1090/S0002-9904-1963-10957-X|doi-access= free}}. An announcement of the index theorem. Reprinted in {{harv|Atiyah|1988c|loc=paper 56}}.
*{{Citation|last1= Atiyah|first1= Michael F. |last2=Singer|first2= Isadore M. |title=The Index of Elliptic Operators I|journal= [[Annals of Mathematics]] |volume=87|pages= 484–530|year= 1968a|doi= 10.2307/1970715|issue= 3|jstor=1970715}}. This gives a proof using K-theory instead of [[cohomology]]. Reprinted in {{harv|Atiyah|1988c|loc=paper 64}}.
*{{Citation |first1=Michael F. |last1=Atiyah|first2= Graeme B.|last2= Segal |title=The Index of Elliptic Operators: II|journal= [[Annals of Mathematics]] | series = Second Series|volume= 87 |issue=3|year= 1968|pages= 531–545 |doi=10.2307/1970716 |jstor=1970716}}. This reformulates the result as a sort of Lefschetz fixed point theorem, using [[K-theory|equivariant K-theory]]. Reprinted in {{harv|Atiyah|1988c|loc=paper 65}}.
*{{Citation|last1= Atiyah|first1= Michael F. |last2=Singer|first2= Isadore M. |title=The Index of Elliptic Operators III|journal=[[Annals of Mathematics]] | series = Second Series|volume= 87|issue=3|year= 1968b|pages= 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 {{harv|Atiyah|1988c|loc=paper 66}}.
*{{Citation|last1= Atiyah|first1= Michael F. |last2=Singer|first2= Isadore M. |title=The Index of Elliptic Operators IV|journal= Annals of Mathematics | series = Second Series|volume= 93|issue=1|year= 1971|pages= 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 {{harv|Atiyah|1988c|loc=paper 67}}.
*{{Citation|last1= Atiyah|first1= Michael F. |last2=Singer|first2= Isadore M. |title=The Index of Elliptic Operators V|journal=[[Annals of Mathematics]] | series = Second Series|volume= 93|issue= 1|year= 1971|pages= 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 {{harv|Atiyah|1988c|loc=paper 68}}.
*{{Citation|first1=Michael F.|last1= Atiyah|first2= Raoul|last2= Bott |title=A Lefschetz Fixed Point Formula for Elliptic Differential Operators|journal= Bull. Am. Math. Soc. |volume=72 |year=1966|pages= 245–50
|doi=10.1090/S0002-9904-1966-11483-0|issue=2 |doi-access=free}}. This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex. Reprinted in {{harv|Atiyah|1988c|loc=paper 61}}.
*{{Citation|first1=Michael F.|last1= Atiyah|first2= Raoul|last2= Bott |title=A Lefschetz Fixed Point Formula for Elliptic Complexes: I |journal=[[Annals of Mathematics]] | series = Second Series|volume= 86|issue=2 |year= 1967|pages= 374–407|doi=10.2307/1970694|jstor=1970694}} (reprinted in {{harv|Atiyah|1988c|loc=paper 61}})and {{citation|first1=Michael F.|last1= Atiyah|first2= Raoul|last2= Bott |title=A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications
|journal=[[Annals of Mathematics]] | series = Second Series|volume=88|issue=3|year= 1968|pages=451–491|doi=10.2307/1970721|jstor=1970721}}. Reprinted in {{harv|Atiyah|1988c|loc=paper 62}}. These give the proofs and some applications of the results announced in the previous paper.
*{{Citation|mr=0650828 |last1=Atiyah|first1= Michael F.|last2= Bott|first2= Raoul|last3= Patodi|first3= Vijay K.|title= On the heat equation and the index theorem|journal= Invent. Math.|volume= 19 |year=1973|pages= 279–330|doi=10.1007/BF01425417|bibcode = 1973InMat..19..279A|issue=4 |s2cid=115700319|url=https://link.springer.com/content/pdf/10.1007%2FBF01425562.pdf}}; {{citation|mr=0650829|title= Errata |journal=Invent. Math.|volume= 28 |year=1975|pages= 277–280|doi=10.1007/BF01425562|author= Atiyah, Michael F.|last2=Bott|first2=R.|last3=Patodi|first3=V. K.|bibcode = 1975InMat..28..277A|issue=3 |doi-access=free}} Reprinted in {{harv|Atiyah|1988d|loc=paper 79, 79a}}.
*{{Citation|mr=0463358|last1= Atiyah|first1= Michael F.|last2= Schmid|first2= Wilfried |title=A geometric construction of the discrete series for semisimple Lie groups|journal= Invent. Math.|volume= 42 |year=1977|issue= 1|pages= 1–62|doi=10.1007/BF01389783|bibcode = 1977InMat..42....1A |s2cid= 189831012}}; {{citation|mr=0550183|title= Erratum|journal= Invent. Math. |volume= 54 |year=1979|issue= 2|pages=189–192|doi=10.1007/BF01408936|author= Atiyah, Michael F.|last2=Schmid|first2=Wilfried|bibcode = 1979InMat..54..189A |doi-access=free}}. Reprinted in {{harv|Atiyah|1988d|loc=paper 90}}.
*{{Citation | last1=Atiyah | first1=Michael | title=Edinburgh Lectures on Geometry, Analysis and Physics | year=2010| arxiv=1009.4827v1 | bibcode=2010arXiv1009.4827A }}
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