Bulletin of the American Mathematical Society

MathSciNet review: 1567795
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Yuri I. Manin
Title: Gauge field theory and complex geometry
Additional book information: Translated from the Russian by N. Koblitz and J. R. King, Springer-Verlag, Berlin, Heidelberg, 1988, x + 295 pp., $80.00. ISBN 0387-18275-6.

M. F. Atiyah, N. J. Hitchin, V. G. Drinfel′d, and Yu. I. Manin, Construction of instantons, Phys. Lett. A 65 (1978), no. 3, 185–187. MR 598562, DOI 10.1016/0375-9601(78)90141-X

R. J. Baston and L. J. Mason, Conformal gravity, the Einstein equations and spaces of complex null geodesics, Classical Quantum Gravity 4 (1987), no. 4, 815–826. MR 895903

F. A. Berezin and D. A. Leĭtes, Supermanifolds, Dokl. Akad. Nauk SSSR 224 (1975), no. 3, 505–508 (Russian). MR 0402795

Simon K. Donaldson, The geometry of $4$-manifolds, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 43–54. MR 934214

5.

M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987.

6.

J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464.

Bertram Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Lecture Notes in Math., Vol. 570, Springer, Berlin, 1977, pp. 177–306. MR 0580292

Claude LeBrun, Thickenings and gauge fields, Classical Quantum Gravity 3 (1986), no. 6, 1039–1059. MR 868717

Claude LeBrun, Thickenings and conformal gravity, Comm. Math. Phys. 139 (1991), no. 1, 1–43. MR 1116408

Claude LeBrun and Mitchell Rothstein, Moduli of super Riemann surfaces, Comm. Math. Phys. 117 (1988), no. 1, 159–176. MR 946998

11.

Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245.

Roger Penrose and Wolfgang Rindler, Spinors and space-time. Vol. 2, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1986. Spinor and twistor methods in space-time geometry. MR 838301, DOI 10.1017/CBO9780511524486

R. S. Ward, On self-dual gauge fields, Phys. Lett. A 61 (1977), no. 2, 81–82. MR 443823, DOI 10.1016/0375-9601(77)90842-8

14.

E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398.

Edward Witten, Twistor-like transform in ten dimensions, Nuclear Phys. B 266 (1986), no. 2, 245–264. MR 829140, DOI 10.1016/0550-3213(86)90090-8

16.

E. Witten, Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267-302, Amer. Math. Soc., Providence, R. I., 1987.

1.

M. Atiyah, N. Hitchin, V. Drinfeld, and Y. Manin, Construction of instantons, Phys. Lett. 65A (1978), 185-187. MR 0598562

2.

R. Baston and L. Mason, Conformal gravity, the Einstein equations, and spaces of complex null geodesics, Class Quantum Grav. 4 (1987), 815-826. MR 895903

3.

F. Berezin and D. Leites, Supermanifolds, Soviet Math. Dokl. 16 (1975), 1218-1221. MR 402795

4.

S. Donaldson, The geometry of 4-manifolds, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 43-54; Amer. Math. Soc., Providence, R. I., 1987. MR 934214

5.

M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987.

6.

J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464.

7.

B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometric Methods in Mathematicas Physics, Lecture Notes in Math., vol. 570, Springer-Verlag, Berlin and New York, 1977. MR 580292

8.

C. LeBrun, Thickenings and gauge fields, Class. Quantum Grav. 3 (1986), 1039-1059. MR 868717

9.

C. LeBrun, Thickenings and conformal gravity, preprint, 1989. MR 1116408

10.

C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Commun. Math. Phys. 117 (1988), 159-176. MR 946998

11.

Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245.

12.

R. Penrose and W. Rindler, Spinors and space-time, V. 2, spinor and twistor methods in space-time geometry, Cambridge Univ. Press, 1986. MR 838301

13.

R. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. MR 443823

14.

E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398.

15.

E. Witten, Twistor-like transform in ten dimensions, Nucl. Phys. B266 (1986), 245-264. MR 829140

16.

E. Witten, Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267-302, Amer. Math. Soc., Providence, R. I., 1987.