L²-topology and Lagrangians in the space of connections over a Riemann surface
Name
Mrowka_L-2 topology (arxiv).pdf
Size
304.28 KB
Format
Adobe PDF
Checksum (MD5)
3a07772d2736e966a44ec6d7864f0836
Author(s)
Mrowka, Tomasz S.
Wehrheim, Katrin
Alternative Title
L-2-topology and Lagrangians in the space of connections over a Riemann surface
Date Issued
November 2010
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-010-0086-3
