|
Algebraic surfaces and 4-manifolds: Some conjectures and speculations
Author(s):
Robert
Friedman;
John W.
Morgan
Journal:
Bull. Amer. Math. Soc.
18
(1988),
1-19.
MSC (1985):
Primary 57R55, 14J15
MathSciNet review:
919651
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385-404. MR 115006
- 2.
- M. Atiyah, Geometrical aspects of gauge theories, Proc. Int'l. Congr. Math. (Helsinki, 1978), Acad. Sci. Fen., Helsinki, 1980, pp. 881-885. MR 562703
- 3.
- M. Atiyah, N. Hitchin and I. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London 362A (1978), 425-461. MR 506229
- 4.
- R. Barlow, A simply connected surface of general type with pg = 0, Invent. Math. 79 (1985), 293-301. MR 778128
- 5.
- W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984. MR 749574
- 6.
- L. Bers, Quasi-conformal mappings and Teichmüller's theorem, Analytic Functions, (Nevanlinna et. al., eds.), Princeton Univ. Press, Princeton, N.J., 1960. MR 114898
- 7.
- F. Bogomolov, Surfaces of class VIIoand affine geometry, Math. USSR-Izv. 21 (1983), 31-73.
- 8.
- E. Bombieri, Canonical models of surfaces of general type, Publ. Math. Inst. Hautes Études Sci. 42 (1973), 171-219. MR 318163
- 9.
- P. Deligne, P. Griffiths, J. Morgan and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975), 245-274. MR 382702
- 10.
- I. Dolgachev, Algebraic surfaces with pg = q = 0, Algebraic Surfaces, C.I.M.E. 1977, Cortona, Liguori, Napoli, 1981, pp. 97-215.
- 11.
- S. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geom. 18 (1983), 279-315. MR 710056
- 12.
- S. Donaldson, Anti-self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985), 1-26. MR 765366
- 13.
- S. Donaldson, Connections, cohomology, and the intersection forms of 4-manifolds, J. Differential Geom. 24 (1986), 275-341. MR 868974
- 14.
- S. Donaldson, Irrationality and the h-cobordism conjecture, preprint. MR 892034
- 15.
- S. Donaldson, Polynomial invariants for smooth 4-manifolds (in preparation).
- 16.
- M. Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982), 357-454. MR 679066
- 17.
- R. Friedman and J. Morgan, On the diffeomorphism types of certain algebraic surfaces. I, II, J. Differential Geom. (to appear). MR 925124
- 18.
- S. Glashow, Quarks with color and flavor, Sci. Amer. 223 no. 4 (1975), 38-50.
- 19.
- P. Griffiths and J. Harris, Principles of algebraic geometry, New York, Wiley, 1978. MR 507725
- 20.
- J. Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1983), 221-240. MR 700769
- 21.
- J. Harris and D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), 23-86. MR 664324
- 22.
- R. Hartshorne, Algebraic geometry, Springer, New York, 1978. MR 463157
- 23.
- M. Inoue, On surfaces of class VII0, Invent. Math. 24 (1974), 269-310. MR 342734
- 24.
- K. Kodaira, On compact analytic surfaces. II, Ann of Math (2) 77 (1963), 563-626.
- 25.
- K. Kodaira, On the structure of compact complex analytic surfaces. II, Amer. J. Math. 88 (1966), 682-721. MR 205280
- 26.
- K. Kodaira, Complex structures on S1 × S3, Proc. Nat. Acad. Sci. 55 (1966), 240-243. MR 196769
- 27.
- M. Lübke and C. Okonek, Differentiable structures of elliptic surfaces with cyclic fundamental group, preprint. MR 906371
- 28.
- F. Maier, Tulane Univ. thesis, 1987.
- 29.
- R. Mandelbaum, Four-dimensional topology: an introduction, Bull. Amer. Math. Soc. (N.S.) 2 (1980), 1-159. MR 551752
- 30.
- R. Mandelbaum and B. Moishezon, On the topological structure of non-singular algebraic surfaces in CP3, Topology 15 (1976), 23-40. MR 405458
- 31.
- J. Milnor, On simply connected 4-manifolds, Proc. Internat. Sympos. Algebraic Topology, Mexico (1958), 122-128. MR 103472
- 32.
- B. Moishezon, Complex surfaces and connected sums of complex projective planes, Lecture Notes in Math., vol. 603, Springer-Verlag, Berlin and New York, 1972. MR 491730
- 33.
- C. Okonek and A. Van de Ven, Stable bundles and differentiable structures on certain elliptic surfaces, Invent. Math. 86 (1986), 357-370. MR 856849
- 34.
- R. Penrose, The complex geometry of the natural world, Proc. Int'l Congr. Math., Helsinki (1978), 189-194. MR 562607
- 35.
- V. Rokhlin, New results in the theory of four-dimensional manifolds, Dokl. Akad. Nauk. S.S.S.R. 84 (1952), 221-224. MR 52101
- 36.
- J.-P. Serre, Cours d'arithmétique, Presses Universitaires de France, Paris, 1970. MR 255476
- 37.
- D. Sullivan, Infinitesimal computations in topology, Publ. Math. Inst. Hautes Études Sci. 47 (1977), 269-332. MR 646078
- 38.
- C. Taubes, Self-dual Yang-Mills connections on non-self-dual 4-manifolds, J. Differential Geom. 17 (1982), 139-170. MR 658473
- 39.
- O. Teichmüller, Extremale quasikonforme Abbildungen und quadratische differentiale, Preuss. Akad. 22 (1939).
- 40.
- W. Thurston, On the geometry and dynamics of homeomorphisms of surfaces, preprint.
- 41.
- M. Ue, On the diffeomorphism types of elliptic surfaces with multiple fibers, Invent. Math. 84 (1986), 633-643. MR 837531
- 42.
- K. Uhlenbeck, Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982), 11-29. MR 648355
- 43.
- C. T. C. Wall, Diffeomorphisms of 4-manifolds, J. London Math. Soc. 39 (1964), 141-149. MR 163324
- 44.
- S. Weinberg, Unified theory of elementary particle interaction, Sci. Amer. 231, no. 1, (1974), 50-59.
- 45.
- J. H. C. Whitehead, On simply connected, 4-dimensional polyhedra, Comment. Math. Helv. 22 (1949), 48-92. MR 29171
- 46.
- C. N. Yang and R. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954), 191-195. MR 65437
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1985):
57R55, 14J15
Retrieve articles in all Journals with MSC
(1985):
57R55, 14J15
Additional Information:
DOI:
10.1090/S0273-0979-1988-15576-0
PII:
S 0273-0979(1988)15576-0
|