L²-topology and Lagrangians in the space of connections over a Riemann surface
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 compac...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2012
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| Online Access: | http://hdl.handle.net/1721.1/70476 https://orcid.org/0000-0001-9520-6535 |
| _version_ | 1826190188615827456 |
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| author | Mrowka, Tomasz S. Wehrheim, Katrin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S. Wehrheim, Katrin |
| author_sort | Mrowka, Tomasz S. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:36:26Z |
| format | Article |
| id | mit-1721.1/70476 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:36:26Z |
| publishDate | 2012 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/704762022-09-23T13:13:26Z L²-topology and Lagrangians in the space of connections over a Riemann surface L-2-topology and Lagrangians in the space of connections over a Riemann surface Mrowka, Tomasz S. Wehrheim, Katrin Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S. Mrowka, Tomasz S. Wehrheim, Katrin 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. 2012-04-27T22:25:11Z 2012-04-27T22:25:11Z 2010-11 2010-05 Article http://purl.org/eprint/type/JournalArticle 1016-443X 1420-8970 http://hdl.handle.net/1721.1/70476 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 https://orcid.org/0000-0001-9520-6535 en_US http://dx.doi.org/10.1007/s00039-010-0086-3 Geometric and Functional Analysis Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Mrowka, Tomasz S. Wehrheim, Katrin L²-topology and Lagrangians in the space of connections over a Riemann surface |
| title | L²-topology and Lagrangians in the space of connections over a Riemann surface |
| title_full | L²-topology and Lagrangians in the space of connections over a Riemann surface |
| title_fullStr | L²-topology and Lagrangians in the space of connections over a Riemann surface |
| title_full_unstemmed | L²-topology and Lagrangians in the space of connections over a Riemann surface |
| title_short | L²-topology and Lagrangians in the space of connections over a Riemann surface |
| title_sort | l² topology and lagrangians in the space of connections over a riemann surface |
| url | http://hdl.handle.net/1721.1/70476 https://orcid.org/0000-0001-9520-6535 |
| work_keys_str_mv | AT mrowkatomaszs l2topologyandlagrangiansinthespaceofconnectionsoverariemannsurface AT wehrheimkatrin l2topologyandlagrangiansinthespaceofconnectionsoverariemannsurface |