Journal of Differential Geometry

Irrationality and the $h$-cobordism conjecture

S. K. Donaldson

Full-text: Open access

Article information

Source
J. Differential Geom. Volume 26, Number 1 (1987), 141-168.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214441179

Digital Object Identifier
doi:10.4310/jdg/1214441179

Mathematical Reviews number (MathSciNet)
MR892034

Zentralblatt MATH identifier
0631.57010

Subjects
Primary: 57R80: $h$- and $s$-cobordism
Secondary: 32C10 32G13: Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 32J15: Compact surfaces 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc. 58G30

Citation

Donaldson, S. K. Irrationality and the $h$-cobordism conjecture. J. Differential Geom. 26 (1987), no. 1, 141--168. doi:10.4310/jdg/1214441179. https://projecteuclid.org/euclid.jdg/1214441179.


Export citation

References

  • [1] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self duality in four dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978) 425-461.
  • [2] W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, Ergebnisse der Math., Springer-Verlag, Berlin, 1984.
  • [3] S. E. Cappell and J. L. Shaneson, Some new four-manifolds, Ann. of Math. 104 (1976)61-72.
  • [4] I. Dolgachev, On Seven's conjecture on simply connected algebraic surfaces, Dokl. Akad. Nauk SSSR 170 (1966); English transl., Soviet Math. Dokl. 7 (1966) 1169-1172.
  • [5] S. K. Donaldson, An application of gauge theory to four dimensional topology, J. Differential Geometry 18 (1983) 279-315.
  • [6] S. K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc.(3) 50 (1985) 1-26.
  • [7] S. K. Donaldson, La topologie differentielle des surfaces complexes, C. R. Acad. Sci. Paris Ser. Math. 301 (1985) 317-320.
  • [8] S. K. Donaldson, Connections, cohomology and the intersection forms of 4-manifolds, J. Differential Geometry 24 (1986) 275-341.
  • [9] S. K. Donaldson, The orientation of Yang-Mills moduli spaces and four-manifold topology, J. Differential Geometry, to appear.
  • [10] S. K. Donaldson, Polynomial invariants for smooth 4-manifolds, in preparation.
  • [11] M. H. Freedman, The topology of four dimensional manifolds, J. Differential Geometry 17 (1982) 357-453.
  • [12] R. Friedman and J. Morgan, On the diffeomorphism types of certain complex surfaces, preprint.
  • [13] D. S. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, Math. Sci. Res. Inst. Publications, No. 1, Springer, New York, 1984.
  • [14] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978.
  • [15] R. Hartshorne, Stable vector bundles of rank 2 on P3, Math. Ann. 238 (1978) 227-280.
  • [16] M. W. Hirsch, Differential topology, Graduate Texts in Math., No. 33, Springer, New York, 1976.
  • [17] N. J. Hitchin, On the curvature of rational surfaces, Proc. Sympos. Pure Math., Vol. 27, Amer. Math. Soc, Providence, RI, 1975, 65-80.
  • [18] K. Kodaira, On compact complex analytic surfaces. III, Ann. of Math. (2) 78 (1963) 1-40.
  • [19] K. Kodaira, On homotopy K3 surfaces, Essays on Topology and Related Topics (dedicated to G. de Rham), Springer, New York, 1970, 58-69.
  • [20] M. Kuranishi, A new proof for the existence of locally complete families of complex structures, Proc. Complex Analysis (Minneapolis), Springer, Berlin, 1964, 142-56.
  • [21] J. W. Milnor, On simply-connected 4-manifolds, Proc. Internat. Sympos. Algebraic Topology, Mexico, 1958, 122-128.
  • [22] J. W. Milnor and R. Stasheff, Characteristic classes, Ann. of Math. Studies, No. 76, Princeton University Press, Princeton, NJ, 1974.
  • [23] A. Newlander and L. Nirenberg, Complex analytic co-ordinates in almost complex manifolds, Ann. of Math. 65 (1957) 391-404.
  • [24] C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective space, Birkhauser, Boston, 1980.
  • [25] C. Okonek and A. Van de Ven, Stable bundles and differentiable structures on certain elliptic surfaces, Invent. Math. 86 (1986) 357-370.
  • [26] R. L. E. Schwarzenberger, Vector bundles on algebraic surfaces, Proc. London Math. Soc.(3) 11 (1961) 601-623.
  • [27] J.-P. Serre, A course in arithmetic, Springer, Berlin, 1973.
  • [28] C. H. Taubes, Self-dual connections on manifolds with indefinite intersection matrix, J. Differential Geometry 19 (1984) 517-60.
  • [29] C. T. C. Wall, Diffeomorphisms of 4-manifolds, J. London Math. Soc. 39 (1964) 131-140.
  • [30] C. T. C. Wall, On simply-connected A-manifolds, J. London Math. Soc. 39 (1964) 141-149.