We provide an analytical construction of the gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition. This result is a necessary ingredient in studies of the relation between gauged sigma model and nonlinear sigma model, such as the closed or open quantum Kirwan map.
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Characteristic Gluing to the Kerr Family and Application to Spacelike Gluing
- Award ID(s):
- 2005464
- PAR ID:
- 10558579
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 403
- Issue:
- 1
- ISSN:
- 0010-3616
- Page Range / eLocation ID:
- 275 to 327
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We describe a general procedure, based on Gerstenhaber–Schack complexes, for extending to quantized twistor spaces the Donaldson–Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on non-commutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.more » « less
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