Abstract
In this note we prove that the number of irreducible components of Hom (π,G) is the same as π1(G), where π is a surface group andG is complex semisimple. This is established by studying the flat bundles on Riemann surfaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Bibliography
[AB] Atiyah, M. F. and Bott, R., The Yang-Mills equations over a compact Rieman surface,Phil. Trans. Roy. Soc. London,A 308 (1982), 523–615
[Go] Goldman, W. M., Topological components of spaces of representations,Invent. Math. 93 (1988) 557–607
[GM1] Goldman, W. M. and Millson, J. J., Deformations of flat bundles over Kahler manifolds, inGeometry and Topology, Manifolds, Varieties and Knots, C. McCrory and T. Shifrin (eds.),Lecture Notes in Pure and Applied Mathematics,105, Mercer Dekker, New York-Basel (1987), 129–145
[GM2] Goldman, W. M. and Millson, J. J., The deformation theory of representations of fundamental groups of compact Kahler manifolds,Publ. Math. I.H.E.S.
[Gu] Gunning, R. C., Lectures on vector bundles over Riemann surfaces, Princeton university press, 1967
[Ko] Koszul, J. L., Lectures on fiber bundles and differential geometry, Tata Institute of fundamental research, Bombay 1960
[Ra] Ramanathan, A., Moduli for principal bundles, inAlgebraic Geometry. Proceeding, Copenhagen 1978,Lecture Notes in Mathematics,732. Berlin, Heidelberg, New York, Springer 1979
Author information
Authors and Affiliations
Additional information
The present work is partially supported by NSF grant DMS89-04922
Rights and permissions
About this article
Cite this article
Li, J. The space of surface group representations. Manuscripta Math 78, 223–243 (1993). https://doi.org/10.1007/BF02599310
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02599310