Michael Atiyah Collected Works; 6-Volume Set

by Michael Atiyah

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Reprint

ISBN13:

9780198520948

ISBN10:

0198520948

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Hardcover

Pub. Date:

2/17/2005

Publisher(s):

Oxford University Press, USA

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Summary

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject. This six volume set of the collected works of professor Sir Michael Atiyah includes: Collected Works: Volume 1: Early Papers; General papers Collected Works: Volume 2: K-Theory Collected Works: Volume 3: Index Theory: 1 Collected Works: Volume 4: Index Theory: 2 Collected Works: Volume 5: Gauge Theories New for 2004-Collected Works: Volume 6: Publications since 1987, including his work on skyrmions, "Atiyah's axioms" for topological quantum field theories, monopolies, knots, K-Theory, equivalent problems, point particles, and M-Theory.

Author Biography

Sir Michael Atiyah was awarded the Fields Medal in 1966. He was elected a Fellow of the Royal Society in 1962 and received the Royal Medal of the Society in 1968 and its Copley Medal in 1988. He gave the Royal Society's Bakerian Lecture on Global geometry in 1975 and was President of the Royal Society from 1990 to 1995.

EARLY PAPERS

Commentary

(2)

A note on the tangents of a twisted cubic. Proc. Camb. Phil. Soc. 48 (1952), 204--5.

(4)

Complex fibre bundles and ruled surfaces. Proc. Lond. Math. Soc. V (1955), 407--34.

(30)

Formes de seconde espece sur une variete algebrique. Comptes Rendus Acad. Sci. Paris 239 (1954), 1333--5.

(6)

W. V. D. Hodge

Integrals of the second kind on an algebraic variety. Ann. of Math. 62 (1955), 56--91.

(38)

W. V. D. Hodge

On the Krull--Schmidt theorem with application to sheaves. Bull. Soc. Math. France 84 (1956), 307--17.

(14)

Complex analytic connections in fibre bundles. Trans. Am. Math. Soc. 85 (1957), 181--207.

(8)

Vector bundles over an elliptic curve. Proc. Lond. Math. Soc. VII (1957), 414--52

103

(42)

On analytic surfaces with double points. Proc. R. Soc. A, 247 (1958), 237--44.

145

(10)

Some examples of complex manifolds. Bonner Mathematische Schriften Nr. 6 (1958).

155

(34)

GENERAL PAPERS

Commentary

185

(4)

The role of algebraic topology in mathematics. J. Lond. Math. Soc. 41 (1966), 63--9.

189

(10)

Wandel und Fortschritt in der Mathematik, Bild der Wissenschaft 4, Deutschen Verlags-Anstalt, Stuttgart (1969), 315--23.

199

(12)

How research is carried out. Bull. IMA 10 (1974), 232--4.

211

(6)

Global geometry. Bakerian Lecture, 1975. Proc. R. Soc. Lond. A 347 (1976), 291--9.

217

(12)

William Vallance Douglas Hodge 1903--1975. Biog. Mem. Fellows Roy. Soc. Lond. 22 (1976), 169--92.

229

(26)

Singularities of Functions. LMS/IMA Conference on `Excitement in mathematics', Cambridge, 1975, Bull. IMA 12 (1976), 203--6.

255

(6)

Trends in Pure Mathematics. Proc. 3rd Int. Congress on Math. Education, Karlsruhe 1976. 3rd ICME Proc. (1977) 71--4.

261

(16)

The Unity of Mathematics. Bull. Lond. Math. Soc. 10 (1978), 69--76.

277

(10)

What is geometry? (Presidential address). The Mathematical Gazette, 66, (No. 437) (1982), 179--84.

287

(8)

An interview with Michael Atiyah. The Mathematical Intelligencer, Vol. 6, (No. 1) (1984), 9--19.

295

(14)

Speech on conferment of Feltrinelli Prize, Accademia Nazionale dei Lincei (1984), 183--8.

309

(8)

Geometry and analysis in the nineteen eighties. Coll. for the 25th anniversary, IHES (1984).

317

(10)

Mathematics and the computer revolution, (a) Nuova Civilta delle Macchine II (No. 3) (1984), 27--32. (b) The Influence of Computers and Informatics on Mathematics and its Teaching. Cambridge University Press (1986) 43--51.

327

(22)

Identifying progress in mathematics. ESF Conference in Colmar. Cambridge University Press (1985), 24--41.

349

EARLY PAPERS ON K-THEORY

Commentary

(6)

Riemann--Roch theorems for differentiable manifolds. Bull. Am. Math. Soc. 65 (1959), 276--81.

(8)

F. Hirzebruch

Quelques theoremes de non-plongement pour les varietes differentiables. Bull. Soc. Math. France 87 (1959), 383--96.

(16)

F. Hirzebruch

On complex Stiefel manifolds. Proc. Camb. Phil. Soc. 56 (1960), 342--53.

(14)

J. A. Todd

Bott periodicity and the parallelizability of the spheres. Proc. Camb. Phil. Soc. 57 (1961), 223--6.

(6)

F. Hirzebruch

Vector bundles and homogeneous spaces, Proceedings of Symposium in Pure Mathematics, Vol. 3. Amer. Math. Soc. (1961).

(34)

F. Hirzebruch

Characters and cohomology of finite groups. Publ. Math. Institut des Hautes Etudes Scientifiques, Paris (1961), 247--89.

(44)

Cohomologie-operationen und Charakteristische Klassen. Math. Zeit. 77 (1961), 149--87.

129

(42)

F. Hirzebruch

Charakteristische Klassen und Anwendungen. l'Enseignement Mathematiques VII (1962), 187--213.

171

(28)

F. Hirzebruch

Immersions and embeddings of manifolds. Topology 1 (1962), 125--32.

199

(10)

Vector bundles and the Kunneth formula. Topology 1 (1962), 245--8.

209

(6)

Bordism and cobordism. Proc. Camb. Phil. Soc. 57 (1961), 200--8.

215

(12)

Thom complexes. Proc. Lond. Math. Soc. XI (1961), 291--310.

227

(22)

Analytic cycles on complex manifolds, Topology 1 (1962), 25--45.

249

(24)

F. Hirzebruch

The Riemann--Roch theorem for analytic embeddings. Topology 1 (1962), 151--66.

273

(18)

F. Hirzebruch

The Grothendieck ring in geometry and topology. Proceedings of the International Congress of Mathematicians. Almquist & Wiksells, Boktryckeri Aktiebolag, Uppsala (1962), 442--6.

291

(8)

Clifford Modules. Topology 3 (Suppl. 1) (1964), 3--38.

299

(38)

R. Bott

A. Shapiro

On the periodicity theorem for complex vector bundles. Acta Mathematica 112 (1964), 229--47.

337

(22)

R. Bott

On the K-theory of compact Lie groups, Topology 4 (1965), 95--9.

359

(8)

K-theory and the Hopf invariant. Quart. J. Math., Oxford (2), 17 (1966), 31--8.

367

(10)

J. F. Adams

K-theory and reality, Quart. J. Math., Oxford (2), 17 (1966), 367--86.

377

(22)

Power operations in K-theory, Quart. J. Math., Oxford (2), 17 (1966), 165--93.

399

(32)

K-theory. Benjamin, New York (1967).

431

(174)

Bott periodicity and the index of elliptic operators, Quant. J. Math. Oxford (2) 19 (1968), 113--40.

605

(30)

Group representations, λ-rings and the J-homomorphism. Topology 8 (1969), 253--97.

635

(48)

D. O. Tall

Algebraic topology of operators in Hilbert space. Lectures in Modern Analysis and Applications I. Lecture Notes in Mathematics, Springer-Verlag, Berlin 103 (1969), 101--22.

683

(24)

Equivariant K-theory and completion, J. Diff. Geom. 3 (1969), 1--18.

707

(20)

G. B. Segal

Vector fields on manifolds. Arbeitsgemeinschaft fur Forschung des Landes Nordrhein Westfalen, Dusseldorf 1969, 200 (1970), 7--24.

727

(24)

Exponential isomorphisms for λ-rings, Quart. J. Math., Oxford 22 (1971), 371--8.

751

(10)

G. B. Segal

Vector fields with finite singularities, Acta Math. 128 (1972), 1--40.

761

(42)

J. L. Dupont

Elliptic operators and singularities of vector fields, Actes, Congress Intern. Math. 2, Gauthier-Villars Editeur (1970), 207--9.

803

(6)

Compact Lie groups and the stable homotopy of spheres. Topology 13 (1974), 135--42.

809

(10)

Larry Smith

A survey of K-theory. Proc. Conf. on K-theory and operator algebras, Athens, Georgia. Lecture Notes in Mathematics, Springer-Verlag, Berlin, 575 (1977), 1--9.

819

INDEX THEORY: 1

Commentary

The index of elliptic operators on compact manifolds. Bull. Am. Math. Soc. 69 (1963), 422--33.

(14)

I. M. Singer

The index problem for manifolds with boundary. Differential Analysis (papers presented at the Bombay Colloquium 1964), Oxford University Press, 175--86.

(14)

R. Bott

The index theorem for manifolds with boundary, Appendix I in seminar on the Atiyah-Singer index theorem, Annals of Math., Study 57, Princeton Univ. Press (1965), 337--51.

(18)

Algebraic topology and elliptic operators. Comm. Pure Appl. Math. XX (1967), 237--49.

(16)

Global aspects of the theory of elliptic differential operators. Proc. Int. Congress of Mathematicians, Moscow, 1966, 57--64.

(10)

A Lefschetz fixed-point formula for elliptic differential operators. Bull. Am. Math. Soc. 72 (1966), 245--50.

(8)

R. Bott

A Lefschetz fixed-point formula for elliptic complexes I. Ann. of Math. 86 (1967), 374--407.

(36)

R. Bott

A Lefschetz fixed-point formula for elliptic complexes II: Applications. Ann. of Math. 88 (1968), 451--91.

127

(44)

R. Bott

The index of elliptic operators: I. Ann. of Math. 87 (1968), 484--530.

171

(53)

I. M. Singer

The index of elliptic operators: II. Ann. of Math. 87 (1968), 531--45.

224

(15)

G. B. Segal

The index of elliptic operators: III. Ann. of Math. 87 (1968), 546--604.

239

(62)

I. M. Singer

The index of elliptic operators: IV. Ann. of Math. 93 (1971), 119--38.

301

(22)

I. M. Singer

The index of elliptic operators: V. Ann. of Math. 93 (1971), 139--49.

323

(14)

I. M. Singer

Global theory of elliptic operators. Proc. of the Int. Symposium on Functional analysis, Tokyo. University of Tokyo Press (1969), 21--30.

337

(12)

Index theory for skew-adjoint Fredholm operators. Publ. Math. Institut des Hautes Etudes Scientifiques, No. 37 (1969), 305--26.

349

(24)

I. M. Singer

The signature of fibre bundles. Global Analysis, papers in honour of K. Kodaira. University of Tokyo Press and Princeton University Press (1969), 73--84.

373

(14)

Topology of elliptic operators. Global Analysis, Proc. Symp. Pure Math. 16, Amer. Math. Soc. (1970), 101--19.

387

(22)

Resolution of singularities and division of distributions. Comm. Pure Appl. Math. 23 (1970) 145--50.

409

(8)

Spin-manifolds and group actions. Essays on topology and related topics, Memoires dedies a Georges de Rham (ed. A. Haefliger and R. Narasimhan), Springer-Verlag, New York-Berlin (1970), 18--28.

417

(14)

F. Hirzebruch

Riemann surfaces and spin structures. Ann. Sci. Ecole Norm. Sup. 4 (1971), 47--62.

431

(18)

Vector bundles on projective 3-space. Inventiones Math. 35 (1976), 131--53.

449

(26)

E. Rees

The index of elliptic operators. Colloquium Lectures, Amer. Math. Soc., Dallas (1973).

475

(24)

Elliptic operators and compact groups. Lecture Notes in Mathematics, Springer-Verlag, Berlin, 401 (1974), 1--93.

499

INDEX THEORY: 2

Commentary

(10)

On the heat equation and the index theorem. Inventiones Math. 19 (1973), 279--330.

(60)

R. Bott

V. K. Patodi

Errata to the paper: On the heat equation and the index theorem. Inventiones Math. 28 (1975), 277--80.

(6)

R. Bott

V. K. Patodi

Spectral asymmetry and Riemannian geometry. Bull. Lond. Math. Soc. 5 (1973), 229--34.

(10)

V. K. Patodi

I. M. Singer

Spectral asymmetry and Riemannian geometry: I. Math. Proc. Camb. Phil. Soc. 77 (1975), 43--69.

(28)

V. K. Patodi

I. M. Singer

Spectral asymmetry and Riemannian geometry: II. Math Proc. Camb. Phil. Soc. 78 (1975), 405--32.

109

(30)

V. K. Patodi

I. M. Singer

Spectral asymmetry and Riemannian geometry: III. Math. Proc. Camb. Phil. Soc. 79 (1976), 71--99.

139

(32)

V. K. Patodi

I. M. Singer

Hyperbolic differential equations and algebraic geometry. Seminaire Bourbaki 19e annee 1966/67, no. 319. W. A. Benjamin Inc., N.Y., Amsterdam, 1--12.

171

(14)

Lacunas for hyperbolic differential operators with constant coefficients I. Acta Math. 124 (1970), 109--89.

185

(84)

R. Bott

L. Garding

Lacunas for hyperbolic differential operators with constant coefficients II. Acta Math. 131 (1973), 145--206.

269

(64)

R. Bott

L. Garding

Eigenvalues and Riemannian geometry. Manifolds-Tokyo 1973, Proc. Int. Conf. on Manifolds and Related Topics in Topology. University of Tokyo Press (1975), 5--9.

333

(8)

Classical groups and classical differential operators on manifolds: Differential operators on manifolds. CIME, Varenna (1975), 6--48.

341

(46)

Elliptic operators, discrete groups and von Neumann algebras. Soc. Math. de France, Asterisque 32--3 (1976), 43--72.

387

(32)

A geometric construction of the discrete series for semisimple Lie groups. Inventiones Math. 42 (1977), 1--62.

419

(70)

W. Schmid

Erratum to A geometric construction of the discrete series for semisimple Lie groups Inventiones Math. 54 (1979), 189--92.

481

(8)

W. Schmid

Characters of semi-simple Lie groups. (Lecture Notes --- unpublished).

489

(70)

Geometry and analysis of Shimizu L-functions. Proc. Nat. Acad. Sci. USA 79 (1982), 5751.

559

(4)

H. Donnelly

I. M. Singer

Eta invariants, signature defects of cusps and values of L-functions. Annals of Maths. 118 (1983), 131--77.

563

H. Donnelly

I. M. Singer

Signature defects of cusps and values of L-functions: the nonsplit case. Annals of Maths. 119 (1984), 635--637. (Addendum to `Eta invariants, signature defects of cusps, and values of L-functions').

613

H. Donnelly

L. M. Singer

GAUGE THEORIES

Commentary

(6)

Deformations of Instantons. Proc. Nat. Acad. Sci., USA 74 (1977), 2662--3.

(4)

N. J. Hitchin

I. M. Singer

Instantons and algebraic geometry. Commun. Math. Phys. 55 (1977), 117--24.

(10)

R. S. Ward

Construction of instantons. Phys. Lett. 65A (1978), 185--7.

(6)

N. J. Hitchin

V. G. Drinfeld

Y. I. Manin

Self-duality in four dimensional Riemannian geometry. Proc. R. Soc. Lond. A 362 (1978), 425--61.

(40)

N. J. Hitchin

I. M. Singer

Geometrical aspects of gauge theories. Proc. Int. Congress of Mathematicians, Helsinki (1978), Vol. 2., 881--5.

(8)

Geometry of Yang--Mills fields. Lezioni Fermiane, Accademia Nazionale dei Lincei & Scuola Normale Superiore, Pisa (1979).

(100)

Real and complex geometry in four dimensions, The Chern Symposium 1979, Berkeley. Springer-Verlag New York Inc. (1980), 1--10.

175

(12)

Green's functions for self-dual four-manifolds, Advances in Mathematics Supplementary studies, Vol. 7A (1981), 129--58.

187

(32)

Topological aspects of Yang--Mills theory. Commun. Math. Phys. 61 (1978), 97--118.

219

(24)

J. D. S. Jones

Remarks on Morse theory. Recent Developments in Gauge Theories. Plenum Pub. Corp. (1980), 1--5.

243

(8)

Yang-Mills and bundles over algebraic curves, Proc. Indian Acad. Sci. (Math. Sci.), 90 (No. 1) (1981), 11--20.

251

(12)

R. Bott

The Yang-Mills equations over Riemann surfaces. Phil. Trans. R. Soc. Lond. A 308, (1982), 523--615.

263

(96)

R. Bott

Convexity and commuting Hamiltonians, Bull. Lond. Math. Soc. 14 (1981), 1--15.

359

(18)

Angular Momentum, convex polyhedra and algebraic geometry, Proc. Edin. Math. Soc., 26 (1983), 121--38.

377

(16)

Convexity and loop groups, Volume dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday, Progress in Mathematics 36 (1983), 33--64.

393

(34)

A. N. Pressley

The moment map and equivariant cohomology, Topology 23 (No. 1) (1984), 1--28.

427

(30)

R. Bott

The moment map in symplectic geometry. Durham Symposium on Global Riemannian Geometry. Ellis Horwood Ltd. (1984), 43--51.

457

(12)

Gauge theory and algebraic geometry. Proc. of Beijing Symposium on differential geometry and partial differential equations. Science Press, China (1982), 1--20.

469

(22)

The Yang--Mills equations and the structure of 4-manifolds. Durham Symposium on Global Riemannian Geometry. Ellis Horwood Ltd. (1984), 11--17.

491

(10)

Geometry of monopoles. Monopoles in quantum field theory. World Scientific Publishing (1982), 3--20.

501

(20)

Solutions of classical equations in gauge theories: Fundamental interactions and rigorous results. Lectures given at the 1981 International Summer School of Theoretical Physics, Poiana Brasov, Romania. Birkhauser (1982), 207--219.

521

(16)

Low energy scattering of non-Abelian monopoles. Phys. Lett. 107A (No. 1) (1985), 21--5.

537

(8)

N. J. Hitchin

Low-energy scattering of non-Abelian magnetic monopoles. Phil. Trans. R. Soc. Lond. 315 (1985), 459--69.

545

(14)

N. J. Hitchin

Instantons in two and four dimensions. Commun. Math. Phys. 93 (1984), 437--51.

559

(18)

Magnetic monopoles in hyperbolic space, in Proc. of Bombay Colloquium 1984 on Vector Bundles on Algebraic Varieties, Oxford University Press (1987), 1--34.

577

(36)

Anomalies and index theory, Lecture Notes in Physics, Springer-Verlag, 208 (1984), 313--22.

613

(12)

Dirac operators coupled to vector potentials. Proc. Nat. Acad. of Sci. USA 81 (No. 8) (1984), 2597--600.

625

(6)

I. M. Singer

Topological aspects of anomalies. Symposium on Anomalies, Geometry, Topology. World Scientific Press (1984), 22--32.

631

(14)

Commentary of Manin's manuscript `New dimensions in geometry', Lecture notes in mathematics, 1111 (Proc. of 25th Mathematics Arbeitstagung, Bonn 1984), Springer--Verlag (1985), 103--9.

645

(10)

Eigenvalues of the Dirac operator, Lecture notes in mathematics, 1111 (Proc. of 25th Mathematics Arbeitstagung, Bonn 1984), Springer-Verlag (1985), 251--60.

655

(12)

Circular symmetry and stationary-phase approximation, Colloquium in honour of Laurent Schwartz, Vol. 2, Asterisque (1985), 43--60.

667

Michael Atiyah Collected Works; 6-Volume Set

9780198520948

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