The deformation theory of representations of fundamental groups of compact Kähler manifolds
Publications Mathématiques de l'IHÉS, Tome 67 (1988) , pp. 43-96.
     author = {Goldman, William and Millson, John J.},
     title = {The deformation theory of representations of fundamental groups of compact K\"ahler manifolds},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {43--96},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {67},
     year = {1988},
     zbl = {0678.53059},
     mrnumber = {90b:32041},
     language = {en},
     url = {}
Goldman, William M.; Millson, John J. The deformation theory of representations of fundamental groups of compact Kähler manifolds. Publications Mathématiques de l'IHÉS, Tome 67 (1988) , pp. 43-96.

[AMM] Arms, J., Marsden, J., and Moncrief, V., Symmetry and bifurcation of momentum mappings, Commun. Math. Phys., 78 (1981), 455-478. | MR 82m:58028 | Zbl 0486.58008

[A] Artin, M., On solutions to analytic equations, Inv. Math., 5 (1968), 277-291. | MR 38 #344 | Zbl 0172.05301

[AB] Atiyah, M. F. and Bott, R., The Yang-Mills equations over a compact Riemann surface, Phil. Trans. Roy. Soc. London, A 308 (1982), 523-615. | MR 85k:14006 | Zbl 0509.14014

[Ch] Chern, S. S, Geometry of characteristic classes, in Proceedings of the Thirteenth Biennial Seminar, Canad. Math. Cong., Montreal (1972), 1-40. | MR 51 #6840 | Zbl 0269.57013

[C1] Corlette, K., Flat G-bundles with canonical metrics, J. Diff. Geo. (to appear). | Zbl 0676.58007

[C2] Corlette, K., Gauge theory and representations of Kähler groups, in The Geometry of Group Representations (Proceedings of Amer. Math. Soc. Summer Conference 1987, Boulder, Colorado), Contemp. Math. (to appear). | Zbl 0663.53057

[C3] Corlette, K., Rigid monodromy representations (in preparation).

[DGMS] Deligne, P., Griffiths, P. A., Morgan, J. W. and Sullivan, D., Rational homotopy type of compact Kähler manifolds, Inv. Math., 29 (1975), 245-274. | Zbl 0312.55011

[D] Donaldson, S. K., Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc., 50 (1985), 1-26. | MR 86h:58038 | Zbl 0529.53018

[G1] Goldman, W. M., Representations of fundamental groups of surfaces, in Geometry and Topology, Proceedings, University of Maryland 1983-1984, J. Alexander and J. Harer (eds.), Lecture Notes in Mathematics, 1167, Berlin-Heidelberg-New York, Springer-Verlag (1985), 95-117. | Zbl 0575.57027

[G2] Goldman, W. M., Topological components of spaces of representations, Inv. Math. (to appear). | Zbl 0655.57019

[GM1] Goldman, W. M., and Millson, J. J., Local rigidity of discrete groups acting on complex hyperbolic space, Inv. Math., 88 (1987), 495-520. | MR 88f:22027 | Zbl 0627.22012

[GM2] Goldman, W. M. and Millson, J. J., Deformations of flat bundles over Kähler manifolds, in Geometry and Topology, Manifolds, Varieties and Knots, C. Mccrory and T. Shifrin (eds.), Lecture Notes in Pure and Applied Mathematics, 105, Marcel Dekker, New York-Basel (1987), 129-145. | Zbl 0618.53051

[GM3] Goldman, W. M. and Millson, J. J., Differential graded Lie algebras and singularities of level sets of momentum mapping, (submitted for publication). | Zbl 0724.58028

[GHV] Greub, W., Halperin, S. and Vanstone, R., Connections, Curvature and Cohomology, Vol. II, Pure and Applied Mathematics, 47, New York-London, Academic Press (1973). | Zbl 0335.57001

[Gr] Griffiths, P. A. et al., Topics in Transcendental Algebraic Geometry, Ann. of Math. Studies, 106 (1984), Princeton, New Jersey, Princeton Univ. Press. | MR 86b:14004 | Zbl 0528.00004

[Gu] Gunning, R. C., Complex Analytic Varieties : the Local Parametrization Theorem, Mathematical Notes, Princeton University Press (1970). | MR 42 #7941 | Zbl 0213.35904

[GR] Gunning, R. C. and Rossi, H., Analytic functions of several complex variables, Englewood Cliffs, New Jersey, Prentice-Hall (1965). | MR 31 #4927 | Zbl 0141.08601

[J] Jacobson, N., Basic Algebra II, San Francisco, W. H. Freeman and Company (1980). | MR 81g:00001 | Zbl 0441.16001

[JM] Johnson, D. and Millson, J., Deformation spaces associated to compact hyperbolic manifolds, in Discrete Groups in Geometry and Analysis, Papers in Honor of G. D. Mostow on His Sixtieth Birthday, R. HOWE (ed.), Progress in Mathematics, 67, Boston-Basel-Stuttgart, Birkhäuser (1987), 48-106. | MR 88j:22010 | Zbl 0664.53023

[K] Kobayashi, S., Differential Geometry of Holomorphic Vector Bundles, Princeton University Press and Mathematical Society of Japan (1987). | Zbl 0708.53002

[KN] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Volume 1, Interscience Tracts in Pure and Applied Mathematics, 15 (1963), New York-London, John Wiley & Sons. | MR 27 #2945 | Zbl 0119.37502

[Kz] Kunz, E., Introduction to Commutative Algebra and Algebraic Geometry (1985), Birkhäuser Boston, Inc. | MR 86e:14001 | Zbl 0563.13001

[LM] Lubotzky, A. and Magid, A., Varieties of representations of finitely generated groups, Memoirs A.M.S., 336 (vol. 5) (1985). | MR 87c:20021 | Zbl 0598.14042

[MS] Morgan, J. W. and Shalen, P. B., Valuations, trees and degenerations of hyperbolic structures I, Ann. Math., 120 (1984), 401-476. | MR 86f:57011 | Zbl 0583.57005

[M] Mumford, D., Introduction to Algebraic Geometry, Harvard University lecture notes.

[N] Nadel, A. M., Singularities and Kodaira dimension of the moduli space of flat Hermitian Yang-Mills connections, Harvard University preprint. | Numdam | Zbl 0652.32017

[NR1] Nijenhuis, A. and Richardson, R. W., Cohomology and deformation of algebraic structures, Bull. A.M.S., 70 (1964), 406-411. | MR 31 #2299 | Zbl 0138.26301

[NR2] Nijenhuis, A. and Richardson, R. W., Cohomology and deformations in graded Lie algebras, Bull. A.M.S., 72 (1966), 1-29. | MR 33 #4190 | Zbl 0136.30502

[N] Nomizu, K., On the cohomology ring of compact homogeneous spaces of nilpotent Lie groups, Ann. Math., 59 (1954), 531-538. | MR 16,219c | Zbl 0058.02202

[Sc] Schlessinger, M., Functors of Artin rings, Trans. A.M.S., 130 (1968), 208-222. | MR 36 #184 | Zbl 0167.49503

[SS] Schlessinger, M. and Stasheff, J., Deformation theory and rational homotopy type, University of North Carolina preprint, 1979.

[Si1] Simpson, C. T., Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, Princeton University preprint. | Zbl 0669.58008

[Si2] Simpson, C. T., Higgs bundles and local systems, Princeton University preprint. | Numdam | Zbl 0814.32003

[St] Steenrod, N. E., The topology of fiber bundles, Princeton Mathematical Series 14 (1951), Princeton New Jersey, Princeton University Press. | MR 12,522b | Zbl 0054.07103

[T] Toledo, D., Representations of surface groups in PSU (1, n) with nonvanishing characteristic number, J. Diff. Geo. (to appear).

[UY] Uhlenbeck, K. and Yau, S. T., On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure and Appl. Math., 39 (1986), 257-293. | MR 88i:58154 | Zbl 0615.58045

[W] Wells, R. O., Differential Analysis on Complex Manifolds, Graduate Texts in Math., 65 (1980), Berlin-Heidelberg-New York, Springer-Verlag. | MR 83f:58001 | Zbl 0435.32004

[Wh] Whitney, H., Complex Analytic Varieties (1972), Addison-Wesley Inc., Reading Massachusetts. | MR 52 #8473 | Zbl 0265.32008

[Z1] Zucker, S., Hodge theory with degenerating coefficients, Ann. Math., 109 (1979), 415-476. | MR 81a:14002 | Zbl 0446.14002

[Z2] Zucker, S., Locally homogeneous variations of Hodge structure, L'Ens. Math., 27 (1981), 243-276. | MR 83m:32034 | Zbl 0584.14003