L²-topology and Lagrangians in the space of connections over a Riemann surface
Author(s)
Mrowka, Tomasz S.; Wehrheim, Katrin
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L-2-topology and Lagrangians in the space of connections over a Riemann surface
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We examine the L²-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl lemma of harmonic analysis, and deduce local pathwise connectedness of the gauge orbits. Based on a quantitative version of the connectivity, we generalize compactness results for anti-self-dual instantons with Lagrangian boundary conditions to general gauge-invariant Lagrangian submanifolds. This provides the foundation for the construction of instanton Floer homology for pairs of a 3-manifold with boundary and a Lagrangian in the configuration space over the boundary.
Date issued
2010-11Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Geometric and Functional Analysis
Publisher
Springer-Verlag
Citation
Mrowka, Tomasz S., and Katrin Wehrheim. “L 2-Topology and Lagrangians in the Space of Connections Over a Riemann Surface.” Geometric and Functional Analysis 20.5 (2010): 1278–1305. Web. 27 Apr. 2012. © 2010 Springer-Verlag
Version: Author's final manuscript
ISSN
1016-443X
1420-8970