Title:
|
Moduli spaces of Lie algebroid connections (English) |
Author:
|
Křižka, Libor |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
44 |
Issue:
|
5 |
Year:
|
2008 |
Pages:
|
403-418 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
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. (English) |
Keyword:
|
moduli space |
Keyword:
|
connection |
Keyword:
|
Lie algebroid |
MSC:
|
32G13 |
idZBL:
|
Zbl 1212.32009 |
idMR:
|
MR2501576 |
. |
Date available:
|
2009-01-29T09:16:07Z |
Last updated:
|
2013-09-19 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127126 |
. |
Reference:
|
[1] Cuellar, J., Dynin, A., Dynin, S.: Fredholm operator families - I.Integral Equations Operator Theory (1983), 853–862. Zbl 0522.47010, MR 0719108 |
Reference:
|
[2] Donaldson, S. K., Kronheimer, P. B.: The Geometry of Four-Manifolds.Oxford University Press, 2001. MR 1079726 |
Reference:
|
[3] Dupré, M. J., Glazebrook, J. F.: Infinite dimensional manifold structures on principal bundles.J. Lie Theory 10 (2000), 359–373. MR 1774866 |
Reference:
|
[4] Glöckner, H.: Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups.J. Funct. Anal. 194 (2002), 347–409. Zbl 1022.22021, MR 1934608, 10.1006/jfan.2002.3942 |
Reference:
|
[5] Glöckner, H., Neeb, K. H.: Banach-Lie quotients, enlargibility, and universal complexifications.J. Reine Angew. Math. 560 (2003), 1–28. Zbl 1029.22029, MR 1992799, 10.1515/crll.2003.056 |
Reference:
|
[6] Gualtieri, M.: Generalized complex geometry.2007, math/0703298. |
Reference:
|
[7] Gualtieri, M.: Generalized complex geometry.Ph.D. thesis, Oxford University, 2004. |
Reference:
|
[8] Gukov, S., Witten, E.: Gauge Theory, Ramification, And The Geometric Langlands Program.hep-th/0612073. |
Reference:
|
[9] Hitchin, N. J.: The self-duality equations on a Riemann surface.Proc. London Math. Soc. 55 (1987), 59–126. Zbl 0634.53045, MR 0887284, 10.1112/plms/s3-55.1.59 |
Reference:
|
[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. Zbl 1128.22013, MR 2306566, 10.4310/CNTP.2007.v1.n1.a1 |
Reference:
|
[11] Kobayashi, S.: Differential Geometry of Complex Vector Bundles.Iwanani Shoten, Publishers and Princeton University Press, 1987. Zbl 0708.53002, MR 0909698 |
Reference:
|
[12] Lübke, M., Okonek, C.: Moduli spaces of simple bundles and Hermitian-Einstein connections.Math. Ann. 276 (1987), 663–674. MR 0879544, 10.1007/BF01456994 |
Reference:
|
[13] Lübke, M., Teleman, A.: The Kobayashi-Hitchin Correspondence.World Scientific, 1995. MR 1370660 |
. |