Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
moduli space; connection; Lie algebroid
moduli space; connection; Lie algebroid
Summary:
We shall prove that the moduli space of irreducible Lie algebroid connections over a connected compact manifold has a natural structure of a locally Hausdorff Hilbert manifold. This generalizes some known results for the moduli space of simple semi-connections on a complex vector bundle over a compact complex manifold.
References:
[1] Cuellar, J., Dynin, A., Dynin, S.: Fredholm operator families - I. Integral Equations Operator Theory (1983), 853–862. MR 0719108 | Zbl 0522.47010
[2] Donaldson, S. K., Kronheimer, P. B.: The Geometry of Four-Manifolds. Oxford University Press, 2001. MR 1079726
[3] Dupré, M. J., Glazebrook, J. F.: Infinite dimensional manifold structures on principal bundles. J. Lie Theory 10 (2000), 359–373. MR 1774866
[4] Glöckner, H.: Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups. J. Funct. Anal. 194 (2002), 347–409. DOI 10.1006/jfan.2002.3942 | MR 1934608 | Zbl 1022.22021
[5] Glöckner, H., Neeb, K. H.: Banach-Lie quotients, enlargibility, and universal complexifications. J. Reine Angew. Math. 560 (2003), 1–28. DOI 10.1515/crll.2003.056 | MR 1992799 | Zbl 1029.22029
[6] Gualtieri, M.: Generalized complex geometry. 2007, math/0703298.
[7] Gualtieri, M.: Generalized complex geometry. Ph.D. thesis, Oxford University, 2004.
[8] Gukov, S., Witten, E.: Gauge Theory, Ramification, And The Geometric Langlands Program. hep-th/0612073.
[9] Hitchin, N. J.: The self-duality equations on a Riemann surface. Proc. London Math. Soc. 55 (1987), 59–126. DOI 10.1112/plms/s3-55.1.59 | MR 0887284 | Zbl 0634.53045
[10] Kapustin, A., Witten, E.: Electric-magnetic duality and the geometric langlands program. Communications in Number Theory and Physics 1 (2007), 1–236, hep-th/0604151. DOI 10.4310/CNTP.2007.v1.n1.a1 | MR 2306566 | Zbl 1128.22013
[11] Kobayashi, S.: Differential Geometry of Complex Vector Bundles. Iwanani Shoten, Publishers and Princeton University Press, 1987. MR 0909698 | Zbl 0708.53002
[12] Lübke, M., Okonek, C.: Moduli spaces of simple bundles and Hermitian-Einstein connections. Math. Ann. 276 (1987), 663–674. DOI 10.1007/BF01456994 | MR 0879544
[13] Lübke, M., Teleman, A.: The Kobayashi-Hitchin Correspondence. World Scientific, 1995. MR 1370660
Search
Partner of
