Inventiones mathematicae

, Volume 95, Issue 3, pp 591–600 | Cite as

On manifolds homeomorphic to\(\mathbb{C}P^2 \# 8\overline {\mathbb{C}P} ^2 \)

  • Dieter Kotschick

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AHS] Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four dimensional Riemannian geometry. Proc. R. Soc. London, Ser. A362, 425–461 (1978)Google Scholar
  2. [B] Barlow, R.N.: A simply connected surface of general type withp g=0. Invent. Math.79, 293–301 (1985)Google Scholar
  3. [BPV] Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. Berlin-Heidelberg-New York: Springer 1984Google Scholar
  4. [D1] Donaldson, S.K.: Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. London Math. Soc.50, 1–26 (1985)Google Scholar
  5. [D2] Donaldson, S.K.: Irrationality and theh-cobordism conjecture. J. Differ. Geom.26, 141–168 (1987)Google Scholar
  6. [D3] Donaldson, S.K.: The orientation of Yang-Mills moduli spaces and 4-manifold topology. J. Differ. Geom.26, 397–428 (1987)Google Scholar
  7. [D4] Donaldson, S.K.: Polynomial invariants for smooth four-manifolds. Topology (to appear)Google Scholar
  8. [FS] Fintushel, R., Stern, R.J.:SO(3)-connections and the topology of 4-manifolds. J. Differ. Geom.20, 523–539 (1984)Google Scholar
  9. [FU] Freed, D.S., Uhlenbeck, K.K.: Instantons and Four-manifolds. Berlin-Heidelberg-New York: Springer 1984Google Scholar
  10. [FM] Friedman, R., Morgan, J.W.: On the diffeomorphism types of certain algebraic surfaces I. J. Differ. Geom.27, 297–369 (1988)Google Scholar
  11. [GH] Griffiths, P., Harris, J.: Residues and zero-cycles on algebraic varieties. Ann. Math.108, 461–505 (1978)Google Scholar
  12. [GZ] van der Geer, G. Zagier, D.: The Hilbert Modular group for the Field\(Q\left( {\sqrt {13} } \right)\). Invent Math.42, 93–133 (1977)Google Scholar
  13. [HK] Hambleton, I., Kreck, M.: On the Classification of Topological 4-Manifolds with Finite Fundamental Group. Math. Ann.280, 1–20 (1988)Google Scholar
  14. [K] Kotschick, D.: Oxford Thesis 1989Google Scholar
  15. [OV] Okonek, C., Van de Ven, A.: Stable bundles and differentiable structures on certain algebraic surfaces. Invent. Math.86, 357–370 (1986)Google Scholar
  16. [OV2] Okonek, C., Van de Ven, A.:T-type-invariants associated toPU(2)-bundles and the differentiable structure of Barlow's surface. Invent. Math.95, 601–614 (1989)Google Scholar
  17. [R] Ried, M.: Surfaces withp g=0.K 2=1. J. Fac. Sci. Univ. Tokyo Sec. IA,25, (No. 1) 75–92 (1978)Google Scholar
  18. [S] Schwarzenberger, R.L.E.: Vector bundles on algebraic surfaces. Proc. London Math. Soc. (3)11, 601–622 (1961)Google Scholar
  19. [T] Tyurin, A.N.: Cycles, curves and vector bundles on an algebraic surface. Duke Math. J.54, 1–26 (1987)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Dieter Kotschick
    • 1
  1. 1.Mathematical InstituteOxford UniversityOxfordEngland

Personalised recommendations