Journal of Differential Geometry

Gauge theory on asymptotically periodic {4}-manifolds

Clifford Henry Taubes

Full-text: Open access

Article information

Source
J. Differential Geom. Volume 25, Number 3 (1987), 363-430.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
http://projecteuclid.org/euclid.jdg/1214440981

Digital Object Identifier
doi:10.4310/jdg/1214440981

Mathematical Reviews number (MathSciNet)
MR882829

Zentralblatt MATH identifier
0615.57009

Subjects
Primary: 58G12
Secondary: 32G99: None of the above, but in this section 53C05: Connections, general theory 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 57R55: Differentiable structures

Citation

Taubes, Clifford Henry. Gauge theory on asymptotically periodic {4}-manifolds. J. Differential Geom. 25 (1987), no. 3, 363--430. doi:10.4310/jdg/1214440981. http://projecteuclid.org/euclid.jdg/1214440981.


Export citation

References

  • [1] R. A. Adams, Sobole spaces, Academic Press, New York, 1975.
  • [2] M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in A-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978) 425-461.
  • [3] M. F. Atiyah and J. D. S. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978) 97-118.
  • [4] M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. 87 (1968) 484-530.
  • [5] M. F. Atiyah, I. M. Singer and V. K. Patodi, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43-69.
  • [6] A. Casson, lectures given at Math Sci. Res. Inst., Spring, 1985.
  • [7] S. S. Chern and J. Simons, Some cohomology classes in principal fibre bundles and their application to Riemannian geometry, Proc. Nat. Acad. Sci. U.S.A. 68 (1971) 791-794.
  • [8] S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geometry 18 (1983) 279-315.
  • [9] S. K. Donaldson, Connections, cohomology, and the intersections forms of 4-manifolds, J. Differential Geometry 24 (1986) 275-341.
  • [10] S. K. Donaldson, to appear.
  • [11] R. Fintushel and R. Stern, 50(3) connections and the topologyo f A-manifolds, preprint.
  • [12] D. Freed and K. K. Uhlenbeck, Instantons and four-manifolds, Springer, Berlin, 1984.
  • [13] M. H. Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357-453.
  • [14] M. H. Freedman and L. R. Taylor, A universal smoothing of four-space, J. Differential Geometry 24 (1986) 69-78.
  • [15] R. Gompf, Three exotic R4's and other anomalies, J. Differential Geometry 18 (1983) 317-328.
  • [16] R. Gompf, An infinite set of exotic R4's J. Differential Geometry 21 (1985) 283-300.
  • [17] M. J. Greenberg, Lectures on algebraic topology, Benjamin, 1967.
  • [18] T. Kato, Perturbation theory for linear operators, Springer, Berlin, 1980.
  • [19] V. A. Kondrat'ev, Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc. 16 (1967).
  • [20] U. Koschorke, Infinite dimensional K-theory, Sympos. Pure Math., Vol. 15, Amer. Math. Soc, Providence, RI, 1970.
  • [21] R. B. Lockhart and R. C. McOwen, Elliptic differential operators on non-compact manifolds, preprint.
  • [22] V. G. Maz'ja and B. A. Plamenevski, Estimates in Lp and Holder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Math. Nachr. 81 (1978) 25-82. (Russian)
  • [23] J. W. Milnor and J. D. Stasheff, Characteristic classes, Princeton University Press, Princeton, 1974.
  • [24] T. Parker, Gauge theories on 4-dimensional Riemannian manifolds, Comm. Math. Phys. 85 (1982) 1-40.
  • [25] F. Quinn, Ends of maps III, dimensions 4 and 5, J. Differential Geometry 17 (1982) 503-521.
  • [26] S. Sedlacek, A direct method for minimizing the Yang-Mills functional on -manifolds, Comm. Math. Phys. 86 (1982) 515-527.
  • [27] S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1968) 861-866.
  • [28] C. H. Taubes, Self-dual connections on non-self-dual A-manifolds, J. Differential Geometry 17 (1982) 139-170.
  • [29] C. H. Taubes, Path connected Yang-Mills moduli spaces, J. Differential Geometry 19 (1984) 337-392.
  • [30] C. H. Taubes, Self-dual connections on A-manifolds with indefinite intersection matrix, J. Differential Geometry 19 (1984) 157-560.
  • [31] K. K. Uhlenbeck, Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982) 11-29.
  • [32] K. K. Uhlenbeck, Connections with Lp -bounds on curvature, Comm. Math. Phys. 83 (1982) 31-42.