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On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

Published online by Cambridge University Press:  20 November 2018

Nan-Kuo Ho  and
Chiu-Chu Melissa Liu
Nan-Kuo Ho
Affiliation:
Department of Mathematics, National Cheng-Kung University, Taiwan e-mail: [email protected]
Chiu-Chu Melissa Liu
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA e-mail: [email protected]
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Abstract

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We study the connectedness of the moduli space of gauge equivalence classes of flat $G$-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

Keywords

53moduli space of flat G connections
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 6 , 01 December 2004 , pp. 1228 - 1236
Copyright
Copyright © Canadian Mathematical Society 2004

References

[AMM] Alekseev, A., Malkin, A., and Meinrenken, E., Lie group valued moment maps J. Differential Geom. 48(1998), 445–495.Google Scholar
[AMW] Alekseev, A., Meinrenken, E., and C.Woodward, Duistermaat-Heckman measures and moduli spaces of flat bundles over surfaces Geom. Funct. Anal. 12(2002), 1–31.Google Scholar
[BD] Bröcker, Theodor and Dieck, Tammo tom, Representations of compact Lie groups. Graduate Texts in Mathematics 98, Springer-Verlag, New York, 1985.Google Scholar
[HM] Hofmann, K.H. and Morris, S.A., The structure of compact groups. A primer for the student—a handbook for the expert. de Gruyter Studies in Mathematics 25, Walter de Gruyter, Berlin, 1998.Google Scholar
[G] Goldman, W.M., The symplectic nature of fundamental groups of surfaces. Adv. in Math. 54(1984), 200–225.Google Scholar
[HL] Ho, N.-K. and Liu, C.-C. M., Connected Components of the Space of Surface Group Representations. Int. Math. Res. Not. (2003), 2359–2372.Google Scholar
[Hu] Humphreys, J.E., Reflection Groups and Coxter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge, 1990.Google Scholar
[K] Knapp, A.W., Lie Groups Beyond an Introduction. Progress in Mathematics 140, Birkhäuser, Boston, MA, 1996.Google Scholar
[Li] Li, J., The space of surface group representations. Manuscripta Math. 78(1993), 223–243.Google Scholar