Skip to main content
Log in

A framework for Morse theory for the Yang-Mills functional

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [A-B] Atiyah, M.F., Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond. A308, 523–615 (1982)

    Google Scholar 

  • [A-J] Atiyah, M.F., Jones, J.D.S.: Topological aspects of Yang-Mills theory. Commun. Math. Phys.61, 97–118 (1978)

    Google Scholar 

  • [Au] Aubin, T.: Equations différentielles non linéaire et problème de Yamabe concernant la courbure scailaire. J. Math. Pures Appl.55, 269–296 (1976)

    Google Scholar 

  • [B1] Bahri, A.: The Palais-Smale condition in the Yamabe problem on an open set in ℝn (Preprint)

  • [B2] Bahri, A.: Topological methods for a certain class of functionals and application. J. Funct. Anal.41, 397–427 (1981)

    Google Scholar 

  • [B-B] Bahri, A., Berestyski, H.: Forced vibrations in super quadratic Hamiltonian systems. Acta Math.152, 143–197 (1984)

    Google Scholar 

  • [B-C1] Bahri, A., Coron, J.C.: Une théorie des points critiques à l'infini pour l'équation de Yamabe et le problème de Kazdan-Warner. C.R. Acad. Sci. Paris3001, 513–516 (1985)

    Google Scholar 

  • [B-C2] Bahri, A., Coron, J.C.: Vers une théorie des points critiques à l'infini. Séminaire Equations aux Dérivées Partielles. Ecole Polytechnique Exposé n0 8, Nov, 1984

  • [B-L] Bourguignon, J.P., Lawson, H.B.: Yang-Mills theory; its physical origin and differential geometric aspects. In: Yau, S.-T. (ed.) Seminar on Differential Geometry, Ann. Math. Stud.102, Princeton, 1982

  • [B-N] Brezis, H., Nirenberg, L.: Positive solutions of non-linear elliptic equations involving critical exponents. Commun. Pure Appl. Math.36, 437–477 (1983)

    Google Scholar 

  • [D1] Donaldson, S.K.: An application of gauge theory to the topology of 4-manifolds. J. Differ. Geom.18, 279–315 (1983)

    Google Scholar 

  • [D2] Donaldson, S.K.: Connections, cohomology and the intersection forms of 4-manifolds. J. Differ. Geom.24, 275–341 (1986)

    Google Scholar 

  • [D3] Donaldson, S.K.: The orientation of Yang-Mills moduli spaces and 4-manifold topology. J. Differ. Geom.26, 397–428 (1987)

    Google Scholar 

  • [D4] Donaldson, S.K.: Irrationality and theh-cobordism conjecture. J. Differ. Geom.26, 141–168 (1987)

    Google Scholar 

  • [F-S] Fintushel, R., Stern, R.: SO(3) connections and the geometry of 4-manifolds. J. Differ. Geom.20, 523–539 (1984)

    Google Scholar 

  • [F-U] Freed, U., Uhlenbeck, K.K.: Instantons and Four-Manifolds. Berlin Heidelberg New York: Springer, 1964

    Google Scholar 

  • [Ka] Kato, T.: Perturbation Theory for Linear Operators. 2nd Ed., Berlin Heidelberg New York: Springer, 1980

    Google Scholar 

  • [M-P] Marino, A., Prodi, G.: Metodi Perturbattivi nella teoria di Morse. Boll. Un. Mat. Ital.11, 1–32 (1975)

    Google Scholar 

  • [Mi] Milnor, J.: Morse Theory. Princeton: Princeton University Press, 1963

    Google Scholar 

  • [Mor] Morrey, C.B.: Multiple Integrals in the Calculus of Variations. Berlin Heidelberg New York: Springer, 1966

    Google Scholar 

  • [Pal1] Palais, R.: Critical point theory and min-max principle. Proc. Symp. Pure. Math.,15, Am. Math. Soc., Providence, RI, 1970

    Google Scholar 

  • [Pal2] Palais, R.: Ljusternik-Snirelman theory on Banach manifolds. Topology5, 115–132 (1966)

    Article  Google Scholar 

  • [Par] Parker, T.: Gauge theories on 4-dimensional Riemannian manifolds. Commun. Math. Phys.85, 563–602 (1982)

    Google Scholar 

  • [S-S] Schrader, R., Seiler, R.: A uniform lower bound on the renormalized scalar Euclidean functional determinant. Commun. Math. Phys.61, 169–175 (1978)

    Google Scholar 

  • [S-U] Sacks, J., Uhlenbeck, K.K.: The existence of minimal 2-spheres. Ann. Math. (2)113, 1–24 (1981)

    Google Scholar 

  • [Sch] Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom.20, 479–495 (1984)

    Google Scholar 

  • [Sed] Sedlacek, S.: A direct method for minimizing the Yang-Mills functional over 4-manifolds. Commun. Math. Phys.86, 515–527 (1982)

    Google Scholar 

  • [S-Y] Siu, Y.T., Yau, S.T.: Compact Kahler manifolds of positive bisectional curvature. Invent. Math.59, 189–204 (1980).

    Google Scholar 

  • [Ta1] Taubes, C.H.: Path-connected Yang-Mills moduli spaces. J. Differ. Geom.19, 337–392 (1984)

    Google Scholar 

  • [Ta2] Taubes, C.H.: Stability in Yang-Mills theories. Commun. Math. Phys.91, 235–263 (1983)

    Google Scholar 

  • [Ta3] Taubes, C.H.: Monopoles and maps fromS 2 toS 2; the topology of the configuration space. Commun. Math. Phys.95, 345–391 (1984)

    Google Scholar 

  • [Ta4] Taubes, C.H.: Min-max theory for the Yang-Mills-Higgs equations. Commun. Math. Phys.97, 473–540 (1985)

    Google Scholar 

  • [Ta5] Taubes, C.H.: Self-dual connections on 4-manifolds with indefinite intersection matrix. J. Differ. Geom.19, 517–560 (1984)

    Google Scholar 

  • [Ta6] Taubes, C.H.: Long range forces and the topology of instanton moduli spaces, Colloque in L'honneur de Laurent Schwartz, Vol. II, Astérisque,132, 243–255 (1985)

    Google Scholar 

  • [Ta7] Taubes, C.H.: Stable topology of self-dual moduli spaces. J. Differ. Geom. (to appear)

  • [U1] Uhlenbeck, K.K.: Connections withL p-bounds on curvatures. Commun. Math. Phys.83, 31–42 (1982)

    Google Scholar 

  • [U2] Uhlenbeck, K.K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83, 11–29 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by the National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taubes, C.H. A framework for Morse theory for the Yang-Mills functional. Invent Math 94, 327–402 (1988). https://doi.org/10.1007/BF01394329

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01394329

Keywords

Navigation