Lifting smooth homotopies of orbit spaces

Schwarz, Gerald W.

Publications Mathématiques de l'IHÉS, Tome 51 (1980), pp. 37-135.

[1] E. M. Andreev, E. B. Vinberg, and A. G. Elashvili, Orbits of greatest dimension in semi-simple linear Lie groups, Functional Anal. Appl., 1 (1967), 257-261. | Zbl

[2] E. Bierstone, Lifting isotopies from orbit spaces, Topology, 14 (1975), 245-252. | MR | Zbl

[3] A. Borel, Linear Algebraic Groups, New York, Benjamin (1969). | MR | Zbl

[4] N. Bourbaki, Algèbre, 3rd ed., Paris, Hermann (1962).

[5] N. Bourbaki, Groupes et Algèbres de Lie, Paris, Hermann (1968).

[6] G. E. Bredon, Fixed point sets and orbits of complementary dimension, in Seminar on Transformation Groups, Ann. of Math. Studies, No. 46, Princeton, Princeton Univ. Press (1960), 195-231. | MR

[7] G. E. Bredon, Introduction to Compact Transformation Groups, New York, Academic Press (1972). | MR | Zbl

[8] G. E. Bredon, Biaxial Actions, mimeographed notes, Rutgers University (1974).

[9] C. Chevalley, Theory of Lie Groups, Princeton, Princeton University Press (1946). | Zbl

[10] C. Chevalley, Théorie des Groupes de Lie, t. III, Paris, Hermann (1955). | MR

[11] C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778-782. | MR | Zbl

[12] M. Davis, Smooth Actions of the Classical Groups, thesis, Princeton University (1974).

[13] M. Davis, Regular On, Un, and Spn manifolds, to appear.

[14] M. Davis, Smooth G-manifolds as collections of fiber bundles, Pacific J. Math., 77 (1978), 315-363. | MR | Zbl

[15] M. Davis and W. C. Hsiang, Concordance classes of Un and Spn actions on homotopy spheres, Ann. of Math., 105 (1977), 325-341. | MR | Zbl

[16] M. Davis, W. C. Hsiang, and J. Morgan, Concordance classes of regular O(n)-actions on homotopy spheres, to appear. | Zbl

[17] J. Dieudonné, Topics in Local Algebra, Notre Dame Mathematical Lectures, No. 10, Notre Dame, University of Notre Dame Press (1967). | MR | Zbl

[18] J. Dieudonné and J. Carrell, Invariant Theory, Old and New, New York, Academic Press (1971). | MR | Zbl

[19] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Amer. Math. Soc. Transl., 6 (1957), 111-244. | Zbl

[20] E. B. Dynkin, Maximal subgroups of the classical groups, Amer. Math. Soc. Transl., 6 (1957), 245-378. | Zbl

[21] A. G. Elashvili, Canonical form and stationary subalgebras of points of general position for simple linear Lie groups, Functional Anal. Appl., 6 (1972), 44-53. | MR | Zbl

[22] A. G. Elashvili, Stationary subalgebras of points of the common state for irreducible linear Lie groups, Functional Anal. Appl., 6 (1972), 139-148. | Zbl

[23] D. Erle and W. C. Hsiang, On certain unitary and symplectic actions with three orbit types, Amer. J. Math., 94 (1972), 289-308. | MR | Zbl

[24] G. Glaeser, Racine carrée d'une fonction différentiable, Ann. Inst. Fourier, 13 (1963), 203-210. | Numdam | MR | Zbl

[25] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, Graduate Texts in Mathematics, 14, New York, Springer-Verlag, 1973. | MR | Zbl

[26] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460-472. | MR | Zbl

[27] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., 16 (1955). | MR | Zbl

[28] A. Grothendieck, Cohomologie Locale des Faisceaux Cohérents et Théorèmes de Lefschetz Locaux et Globaux (SGA 2), Amsterdam, North-Holland (1968). | MR | Zbl

[29] A. Grothendieck, Local Cohomology (Notes by R. Hartshorne), Lecture Notes in Mathematics, No. 41, New York, Springer-Verlag (1967). | MR | Zbl

[30] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Englewood Cliffs, Prentice-Hall (1965). | MR | Zbl

[31] G. Hochschild, The Structure of Lie Groups, San Francisco, Holden-Day (1965). | MR | Zbl

[32] G. Hochschild and G. D. Mostow, Representations and representative functions on Lie groups III, Ann. of Math., 70 (1957), 85-100. | MR | Zbl

[33] M. Hochster, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math., 96 (1972), 318-337. | MR | Zbl

[34] M. Hochster and J. A. Eagon, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math., 93 (1971), 1020-1058. | MR | Zbl

[35] M. Hochster and J. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. in Math., 13 (1974), 115-175. | MR | Zbl

[36] W. C. Hsiang and W. Y. Hsiang, Differentiable actions of compact connected classical groups : I, Amer. J. Math., 89 (1967), 705-786. | MR | Zbl

[37] W. C. Hsiang, Differentiable actions of compact connected classical groups : II, Ann. of Math., 92 (1970), 189-223. | MR | Zbl

[38] W. Y. Hsiang, On the principal orbit type and P. A. Smith theory of SU (p) actions, Topology, 6 (1967), 125-135. | MR | Zbl

[39] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, 9, New York, Springer-Verlag (1972). | MR | Zbl

[40] J. E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, 21, New York, Springer-Verlag (1975). | MR | Zbl

[41] K. Jänich, Differenzierbare Mannigfaltigkeiten mit Rand als Orbiträume differenzierbarer G-Mannigfaltigkeiten ohne Rand, Topology, 5 (1966), 301-320. | Zbl

[42] K. Jänich, On the classification of O(n)-manifolds, Math. Ann., 176 (1968), 53-76. | MR | Zbl

[43] B. Kostant, Lie group representations on polynomial rings, Amer. J. Math., 85 (1963), 327-402. | MR | Zbl

[44] M. Krämer, Eine Klassifikation bestimmter Untergruppen kompakter zusammenhängender Liegruppen, Comm. in Alg., 3 (1975), 691-737. | Zbl

[45] M. Krämer, Some tips on the decomposition of tensor product representations of compact connected Lie groups, to appear in Reports on Mathematical Physics. | Zbl

[46] S. Lang, Algebra, Reading, Addison-Wesley (1965). | MR | Zbl

[47] J. A. Leslie, On a differentiable structure for the group of diffeomorphisms, Topology, 6 (1967), 263-271. | MR | Zbl

[48] S. Łojasiewicz, Ensembles Semi-analytiques, Lecture Notes, I.H.E.S. (1965).

[49] D. Luna, Sur les orbites fermées des groupes algébriques réductifs, Invent. Math., 16 (1972), 1-5. | MR | Zbl

[50] D. Luna, Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105. | Numdam | MR | Zbl

[51] D. Luna, Adhérences d'orbite et invariants, Invent. Math., 29 (1975), 231-238. | MR | Zbl

[52] D. Luna, Fonctions différentiables invariantes sous l'opération d'un groupe réductif, Ann. Inst. Fourier, 26 (1976), 33-49. | Numdam | MR | Zbl

[53] B. Malgrange, Division des distributions, Séminaire L. Schwartz (1959-1960), exposés 21-25. | Numdam

[54] B. Malgrange, Ideals of Differentiable Functions, Bombay, Oxford University Press (1966).

[55] J. N. Mather, Stratifications and mappings, in Dynamical Systems, New York, Academic Press (1973), 195-232. | MR | Zbl

[56] J. N. Mather, Differentiable invariants, Topology, 16 (1977), 145-155. | MR | Zbl

[57] G. D. Mostow, Self-adjoint groups, Ann. of Math., 62 (1955), 44-55. | MR | Zbl

[58] D. Mumford, Geometric Invariant Theory, Erg. der Math., Bd 34, New York, Springer-Verlag (1965). | MR | Zbl

[59] D. Mumford, Introduction to Algebraic Geometry, preliminary version, Harvard University (1966).

[60] R. Narasimhan, Introduction to the Theory of Analytic Spaces, Lecture Notes in Mathematics, No. 25, New York, Springer-Verlag (1966). | MR | Zbl

[61] R. S. Palais, The classification of G-spaces, Mem. Amer. Math. Soc., No. 36 (1960). | MR | Zbl

[62] R. S. Palais, Slices and equivariant embeddings, in Seminar on Transformation Groups, Ann. of Math. Studies, No. 46, Princeton, Princeton Univ. Press (1960), 101-115. | MR

[63] R. Richardson, Principal orbit types for algebraic transformation spaces in characteristic zero, Invent. Math., 16 (1972), 6-14. | MR | Zbl

[64] F. Ronga, Stabilité locale des applications équivariantes, in Differential Topology and Geometry, Dijon 1974. Lecture Notes in Mathematics, No. 484, New York, Springer-Verlag (1975), 23-35. | MR | Zbl

[65] M. Schlessinger, Rigidity of quotient singularities, Invent. Math., 14 (1971), 17-26. | MR | Zbl

[66] G. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology, 14 (1975), 63-68. | MR | Zbl

[67] G. Schwarz, Representations of simple Lie groups with regular rings of invariants, Invent. Math., 49 (1978), 167-191. | MR | Zbl

[68] G. Schwarz, Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978), 1-12. | MR | Zbl

[69] A. Seidenberg, A new decision method for elementary algebra, Ann. of Math., 60 (1954), 365-374. | MR | Zbl

[70] J.-P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, 6 (1955-1956), 1-42. | Numdam | MR | Zbl

[71] J.-P. Serre, Algèbre Locale. Multiplicités, Lecture Notes in Mathematics, No. 11, New York, Springer-Verlag (1965). | MR | Zbl

[72] Y. T. Siu, Techniques of Extension of Analytic Objects, Lecture Notes in Pure and Applied Mathematics, No. 8, New York, Marcel Dekker (1974). | MR | Zbl

[73] J.-Cl. Tougeron, Idéaux de Fonctions Différentiables, Erg. der Math., Bd 71, New York, Springer-Verlag (1972). | MR | Zbl

[74] D. Vogt, Charakterisierung der Unterräume von s, Math. Z., 155 (1977), 109-117. | MR | Zbl

[75] D. Vogt, Subspaces and quotient spaces of (s), in Functional Analysis : Surveys and Recent Results, North-Holland Math. Studies, Vol. 27 ; Notas de Mat., No. 63, Amsterdam, North-Holland (1977), 167-187. | MR | Zbl

[76] D. Vogt and M. Wagner, Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau, to appear. | Zbl

[77] Th. Vust, Covariants de groupes algébriques réductifs, thèse, Univ. de Genève (1974).

[78] Th. Vust, Opération de groupes réductifs dans un type de cônes presque homogènes, Bull. Soc. Math. France, 102 (1974), 317-334. | Numdam | MR | Zbl

[79] G. S. Wells, Isotopies of semianalytic spaces of finite type, to appear.

[80] H. Weyl, The Classical Groups, 2nd ed., Princeton, Princeton University Press, 1946.

[81] H. Whitney, Complex Analytic Varieties, Reading, Addison-Wesley (1972). | MR | Zbl