@article{PMIHES_1988__67__43_0, author = {Goldman, William M. 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}, mrnumber = {90b:32041}, zbl = {0678.53059}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1988__67__43_0/} }
TY - JOUR AU - Goldman, William M. AU - Millson, John J. TI - The deformation theory of representations of fundamental groups of compact Kähler manifolds JO - Publications Mathématiques de l'IHÉS PY - 1988 SP - 43 EP - 96 VL - 67 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_1988__67__43_0/ LA - en ID - PMIHES_1988__67__43_0 ER -
%0 Journal Article %A Goldman, William M. %A Millson, John J. %T The deformation theory of representations of fundamental groups of compact Kähler manifolds %J Publications Mathématiques de l'IHÉS %D 1988 %P 43-96 %V 67 %I Institut des Hautes Études Scientifiques %U http://www.numdam.org/item/PMIHES_1988__67__43_0/ %G en %F PMIHES_1988__67__43_0
Goldman, William M.; Millson, John J. The deformation theory of representations of fundamental groups of compact Kähler manifolds. Publications Mathématiques de l'IHÉS, Volume 67 (1988), pp. 43-96. http://www.numdam.org/item/PMIHES_1988__67__43_0/
[AMM] Symmetry and bifurcation of momentum mappings, Commun. Math. Phys., 78 (1981), 455-478. | MR | Zbl
, , and ,[A] On solutions to analytic equations, Inv. Math., 5 (1968), 277-291. | MR | Zbl
,[AB] The Yang-Mills equations over a compact Riemann surface, Phil. Trans. Roy. Soc. London, A 308 (1982), 523-615. | MR | Zbl
and ,[Ch] Geometry of characteristic classes, in Proceedings of the Thirteenth Biennial Seminar, Canad. Math. Cong., Montreal (1972), 1-40. | MR | Zbl
,[C1] Flat G-bundles with canonical metrics, J. Diff. Geo. (to appear). | Zbl
,[C2] 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
,[C3] Rigid monodromy representations (in preparation).
,[DGMS] Rational homotopy type of compact Kähler manifolds, Inv. Math., 29 (1975), 245-274. | Zbl
, , , and ,[D] Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc., 50 (1985), 1-26. | MR | Zbl
,[G1] Representations of fundamental groups of surfaces, in Geometry and Topology, Proceedings, University of Maryland 1983-1984, and (eds.), Lecture Notes in Mathematics, 1167, Berlin-Heidelberg-New York, Springer-Verlag (1985), 95-117. | Zbl
,[G2] Topological components of spaces of representations, Inv. Math. (to appear). | Zbl
,[GM1] Local rigidity of discrete groups acting on complex hyperbolic space, Inv. Math., 88 (1987), 495-520. | MR | Zbl
, and ,[GM2] Deformations of flat bundles over Kähler manifolds, in Geometry and Topology, Manifolds, Varieties and Knots, and (eds.), Lecture Notes in Pure and Applied Mathematics, 105, Marcel Dekker, New York-Basel (1987), 129-145. | Zbl
and ,[GM3] Differential graded Lie algebras and singularities of level sets of momentum mapping, (submitted for publication). | Zbl
and ,[GHV] Connections, Curvature and Cohomology, Vol. II, Pure and Applied Mathematics, 47, New York-London, Academic Press (1973). | Zbl
, and ,[Gr] Topics in Transcendental Algebraic Geometry, Ann. of Math. Studies, 106 (1984), Princeton, New Jersey, Princeton Univ. Press. | MR | Zbl
et al.,[Gu] Complex Analytic Varieties : the Local Parametrization Theorem, Mathematical Notes, Princeton University Press (1970). | MR | Zbl
,[GR] Analytic functions of several complex variables, Englewood Cliffs, New Jersey, Prentice-Hall (1965). | MR | Zbl
and ,[J] Basic Algebra II, San Francisco, W. H. Freeman and Company (1980). | MR | Zbl
,[JM] 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 | Zbl
and ,[K] Differential Geometry of Holomorphic Vector Bundles, Princeton University Press and Mathematical Society of Japan (1987). | Zbl
,[KN] Foundations of Differential Geometry, Volume 1, Interscience Tracts in Pure and Applied Mathematics, 15 (1963), New York-London, John Wiley & Sons. | MR | Zbl
and ,[Kz] Introduction to Commutative Algebra and Algebraic Geometry (1985), Birkhäuser Boston, Inc. | MR | Zbl
,[LM] Varieties of representations of finitely generated groups, Memoirs A.M.S., 336 (vol. 5) (1985). | MR | Zbl
and ,[MS] Valuations, trees and degenerations of hyperbolic structures I, Ann. Math., 120 (1984), 401-476. | MR | Zbl
and ,[M] Introduction to Algebraic Geometry, Harvard University lecture notes.
,[N] Singularities and Kodaira dimension of the moduli space of flat Hermitian Yang-Mills connections, Harvard University preprint. | Numdam | Zbl
,[NR1] Cohomology and deformation of algebraic structures, Bull. A.M.S., 70 (1964), 406-411. | MR | Zbl
and ,[NR2] Cohomology and deformations in graded Lie algebras, Bull. A.M.S., 72 (1966), 1-29. | MR | Zbl
and ,[N] On the cohomology ring of compact homogeneous spaces of nilpotent Lie groups, Ann. Math., 59 (1954), 531-538. | MR | Zbl
,[Sc] Functors of Artin rings, Trans. A.M.S., 130 (1968), 208-222. | MR | Zbl
,[SS] Deformation theory and rational homotopy type, University of North Carolina preprint, 1979.
and ,[Si1] Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, Princeton University preprint. | Zbl
,[Si2] Higgs bundles and local systems, Princeton University preprint. | Numdam | Zbl
,[St] The topology of fiber bundles, Princeton Mathematical Series 14 (1951), Princeton New Jersey, Princeton University Press. | MR | Zbl
,[T] Representations of surface groups in PSU (1, n) with nonvanishing characteristic number, J. Diff. Geo. (to appear).
,[UY] On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure and Appl. Math., 39 (1986), 257-293. | MR | Zbl
and ,[W] Differential Analysis on Complex Manifolds, Graduate Texts in Math., 65 (1980), Berlin-Heidelberg-New York, Springer-Verlag. | MR | Zbl
,[Wh] Complex Analytic Varieties (1972), Addison-Wesley Inc., Reading Massachusetts. | MR | Zbl
,[Z1] Hodge theory with degenerating coefficients, Ann. Math., 109 (1979), 415-476. | MR | Zbl
,[Z2] Locally homogeneous variations of Hodge structure, L'Ens. Math., 27 (1981), 243-276. | MR | Zbl
,