The deformation theory of representations of fundamental groups of compact Kähler manifolds
William M. Goldman; John J. Millson
Publications Mathématiques de l'IHÉS (1988)
- Volume: 67, page 43-96
- ISSN: 0073-8301
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topGoldman, William M., and Millson, John J.. "The deformation theory of representations of fundamental groups of compact Kähler manifolds." Publications Mathématiques de l'IHÉS 67 (1988): 43-96. <http://eudml.org/doc/104031>.
@article{Goldman1988,
author = {Goldman, William M., Millson, John J.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {fundamental group; Kähler manifold; affine variety; cup product; Lie product; Hodge structure; Hermitian symmetric space; deformation problem},
language = {eng},
pages = {43-96},
publisher = {Institut des Hautes Études Scientifiques},
title = {The deformation theory of representations of fundamental groups of compact Kähler manifolds},
url = {http://eudml.org/doc/104031},
volume = {67},
year = {1988},
}
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
PB - Institut des Hautes Études Scientifiques
VL - 67
SP - 43
EP - 96
LA - eng
KW - fundamental group; Kähler manifold; affine variety; cup product; Lie product; Hodge structure; Hermitian symmetric space; deformation problem
UR - http://eudml.org/doc/104031
ER -
References
top- [AMM] ARMS, J., MARSDEN, J., and MONCRIEF, V., Symmetry and bifurcation of momentum mappings, Commun. Math. Phys., 78 (1981), 455-478. Zbl0486.58008MR82m:58028
- [A] ARTIN, M., On solutions to analytic equations, Inv. Math., 5 (1968), 277-291. Zbl0172.05301MR38 #344
- [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. Zbl0509.14014MR85k:14006
- [Ch] CHERN, S. S, Geometry of characteristic classes, in Proceedings of the Thirteenth Biennial Seminar, Canad. Math. Cong., Montreal (1972), 1-40. Zbl0269.57013MR51 #6840
- [C1] CORLETTE, K., Flat G-bundles with canonical metrics, J. Diff. Geo. (to appear). Zbl0676.58007
- [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). Zbl0663.53057
- [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. Zbl0312.55011
- [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. Zbl0529.53018MR86h:58038
- [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. Zbl0575.57027
- [G2] GOLDMAN, W. M., Topological components of spaces of representations, Inv. Math. (to appear). Zbl0655.57019
- [GM1] GOLDMAN, W. M., and MILLSON, J. J., Local rigidity of discrete groups acting on complex hyperbolic space, Inv. Math., 88 (1987), 495-520. Zbl0627.22012MR88f:22027
- [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. Zbl0618.53051
- [GM3] GOLDMAN, W. M. and MILLSON, J. J., Differential graded Lie algebras and singularities of level sets of momentum mapping, (submitted for publication). Zbl0724.58028
- [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). Zbl0335.57001
- [Gr] GRIFFITHS, P. A. et al., Topics in Transcendental Algebraic Geometry, Ann. of Math. Studies, 106 (1984), Princeton, New Jersey, Princeton Univ. Press. Zbl0528.00004MR86b:14004
- [Gu] GUNNING, R. C., Complex Analytic Varieties : the Local Parametrization Theorem, Mathematical Notes, Princeton University Press (1970). Zbl0213.35904MR42 #7941
- [GR] GUNNING, R. C. and ROSSI, H., Analytic functions of several complex variables, Englewood Cliffs, New Jersey, Prentice-Hall (1965). Zbl0141.08601MR31 #4927
- [J] JACOBSON, N., Basic Algebra II, San Francisco, W. H. Freeman and Company (1980). Zbl0441.16001MR81g:00001
- [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. Zbl0664.53023MR88j:22010
- [K] KOBAYASHI, S., Differential Geometry of Holomorphic Vector Bundles, Princeton University Press and Mathematical Society of Japan (1987). Zbl0708.53002
- [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. Zbl0119.37502MR27 #2945
- [Kz] KUNZ, E., Introduction to Commutative Algebra and Algebraic Geometry (1985), Birkhäuser Boston, Inc. Zbl0563.13001MR86e:14001
- [LM] LUBOTZKY, A. and MAGID, A., Varieties of representations of finitely generated groups, Memoirs A.M.S., 336 (vol. 5) (1985). Zbl0598.14042MR87c:20021
- [MS] MORGAN, J. W. and SHALEN, P. B., Valuations, trees and degenerations of hyperbolic structures I, Ann. Math., 120 (1984), 401-476. Zbl0583.57005MR86f:57011
- [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. Zbl0652.32017
- [NR1] NIJENHUIS, A. and RICHARDSON, R. W., Cohomology and deformation of algebraic structures, Bull. A.M.S., 70 (1964), 406-411. Zbl0138.26301MR31 #2299
- [NR2] NIJENHUIS, A. and RICHARDSON, R. W., Cohomology and deformations in graded Lie algebras, Bull. A.M.S., 72 (1966), 1-29. Zbl0136.30502MR33 #4190
- [N] NOMIZU, K., On the cohomology ring of compact homogeneous spaces of nilpotent Lie groups, Ann. Math., 59 (1954), 531-538. Zbl0058.02202MR16,219c
- [Sc] SCHLESSINGER, M., Functors of Artin rings, Trans. A.M.S., 130 (1968), 208-222. Zbl0167.49503MR36 #184
- [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. Zbl0669.58008
- [Si2] SIMPSON, C. T., Higgs bundles and local systems, Princeton University preprint. Zbl0814.32003
- [St] STEENROD, N. E., The topology of fiber bundles, Princeton Mathematical Series 14 (1951), Princeton New Jersey, Princeton University Press. Zbl0054.07103MR12,522b
- [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. Zbl0615.58045MR88i:58154
- [W] WELLS, R. O., Differential Analysis on Complex Manifolds, Graduate Texts in Math., 65 (1980), Berlin-Heidelberg-New York, Springer-Verlag. Zbl0435.32004MR83f:58001
- [Wh] WHITNEY, H., Complex Analytic Varieties (1972), Addison-Wesley Inc., Reading Massachusetts. Zbl0265.32008MR52 #8473
- [Z1] ZUCKER, S., Hodge theory with degenerating coefficients, Ann. Math., 109 (1979), 415-476. Zbl0446.14002MR81a:14002
- [Z2] ZUCKER, S., Locally homogeneous variations of Hodge structure, L'Ens. Math., 27 (1981), 243-276. Zbl0584.14003MR83m:32034
Citations in EuDML Documents
top- Michael Kapovich, John J. Millson, The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces
- Ziv Ran, Semiregularity, obstructions and deformations of Hodge classes
- Elena Martinengo, Local Structure of Brill-Noether Strata in the Moduli Space of Flat Stable Bundles
- Marco Manetti, Lie description of higher obstructions to deforming submanifolds
- Jonathan Pridham, The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
- João Pedro P. dos Santos, Lifting -modules from positive to zero characteristic
- Olivier Biquard, Fibrés de Higgs et connexions intégrables : le cas logarithmique (diviseur lisse)
- Pierre Pansu, Sous-groupes discrets des groupes de Lie : rigidité, arithméticité
- Carlos T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety I
- Carlos T. Simpson, Higgs bundles and local systems
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