Abstract
We study bubbling phenomena of anti-self-dual instantons on 
where Σ is a closed Riemann surface. The instantons satisfy a global Lagrangian boundary condition on each boundary slice 
. The main results establish the energy quantization and removal of singularities near such boundary slices. This completes the analytic foundations for the definition of a new instanton Floer homology for 3-manifolds with boundary. In the interior case, for anti-self-instantons on 
our methods provide a new approach to the removable singularity theorem by Sibner-Sibner for codimension 2 singularities with a holonomy condition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, R.A.: Sobolev Spaces. New York, Academic Press, 1978
Bourguignon, J.-P., Lawson Jr., H.B.: Stability and Isolation Phenomena for Yang-Mills Fields. Commun. Math. Phys. 79, 189–230 (1981)
Donaldson, S.K.: Polynomial invariants of smooth four-manifolds. Topology 29, 257–315 (1990)
Floer, A.: An instanton invariant for 3-manifolds. Commun. Math. Phys. 118, 215–240 (1988)
Fukaya, K.: Floer homology for 3-manifolds with boundary I, Preprint, 1997. http://www.kusm. kyoto-u.ac.jp/∼fukaya/fukaya.html
Hofmann, K.H., Morris, S.A.: The structure of compact groups. de Gruyter Studies in Mathematics, Berlin: de Gruyter, 1998
Hang, F.B., Lin, F.H.: A Liouville type theorem for minimizing maps. Methods and Applications of Analysis, to appear
Hardt, R., Lin, F.H.: Mappings minimizing the Lp-norm of the gradient. Comm. Pure Appl. Math. 40(5), 555–588 (1987)
Hofer, H., Zehnder, E.: Symplectic Invariants and Hamiltonian Dynamics. Basel-Boston: Birkhäuser, 1994
Kronheimer, P.B., Mrowka, T.S.: Gauge theory for embedded surfaces I. Topology 32(4), 773–826 (1993)
Rade, J.: Singular Yang-Mills fields. Local theory II. J. reine angew. Math. 456, 197–219 (1994)
Salamon, D.A.: Lagrangian intersections, 3-manifolds with boundary, and the Atiyah–Floer conjecture. In: Proceedings of the ICM, Zürich, 1994, Basel: Birkhäuser, 1995, Vol. 1, pp. 526–536
Sibner, L.M., Sibner, R.J.: Classification of singular Sobolev connections by their holonomy. Comm. Math. Phys. 144, 337–350 (1992)
Uhlenbeck, K.K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys. 83, 11–29 (1982)
Uhlenbeck, K.K.: Connections with Lp-bounds on curvature. Commun. Math. Phys. 83, 31–42 (1982)
Wehrheim, K.: Uhlenbeck Compactness. EMS Series of Lectures in Mathematics, 2004
Wehrheim, K.: Banach space valued Cauchy-Riemann equations with totally real boundary conditions. Comm. Contemp. Math. 6(4), 601–635 (2004)
Wehrheim, K.: Anti-self-dual instantons with Lagrangian boundary conditions I: Elliptic theory. Comm. Math. Phys. 254(1), 45–89 (2005)
Wehrheim, K.: Energy quantization and mean value inequalities for nonlinear boundary value problems. To appear in J.Eur.Math.Soc.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by N.A. Nekrasov
Rights and permissions
About this article
Cite this article
Wehrheim, K. Anti-Self-Dual Instantons with Lagrangian Boundary Conditions II: Bubbling. Commun. Math. Phys. 258, 275–315 (2005). https://doi.org/10.1007/s00220-005-1349-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-005-1349-y