Lifting smooth homotopies of orbit spaces
Publications Mathématiques de l'IHÉS (1980)
- Volume: 51, page 37-135
- ISSN: 0073-8301
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topSchwarz, Gerald W.. "Lifting smooth homotopies of orbit spaces." Publications Mathématiques de l'IHÉS 51 (1980): 37-135. <http://eudml.org/doc/103968>.
@article{Schwarz1980,
author = {Schwarz, Gerald W.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {lifting smooth homotopies of orbit spaces; smooth analogue of Palais' covering homotopy theorem; isotopy lifting conjecture; smooth actions of compact Lie groups},
language = {eng},
pages = {37-135},
publisher = {Institut des Hautes Études Scientifiques},
title = {Lifting smooth homotopies of orbit spaces},
url = {http://eudml.org/doc/103968},
volume = {51},
year = {1980},
}
TY - JOUR
AU - Schwarz, Gerald W.
TI - Lifting smooth homotopies of orbit spaces
JO - Publications Mathématiques de l'IHÉS
PY - 1980
PB - Institut des Hautes Études Scientifiques
VL - 51
SP - 37
EP - 135
LA - eng
KW - lifting smooth homotopies of orbit spaces; smooth analogue of Palais' covering homotopy theorem; isotopy lifting conjecture; smooth actions of compact Lie groups
UR - http://eudml.org/doc/103968
ER -
References
top- [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. Zbl0176.30301
- [2] E. BIERSTONE, Lifting isotopies from orbit spaces, Topology, 14 (1975), 245-252. Zbl0317.57015MR51 #11551
- [3] A. BOREL, Linear Algebraic Groups, New York, Benjamin (1969). Zbl0186.33201MR40 #4273
- [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. MR22 #7129
- [7] G. E. BREDON, Introduction to Compact Transformation Groups, New York, Academic Press (1972). Zbl0246.57017MR54 #1265
- [8] G. E. BREDON, Biaxial Actions, mimeographed notes, Rutgers University (1974).
- [9] C. CHEVALLEY, Theory of Lie Groups, Princeton, Princeton University Press (1946). Zbl0063.00842
- [10] C. CHEVALLEY, Théorie des Groupes de Lie, t. III, Paris, Hermann (1955).
- [11] C. CHEVALLEY, Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778-782. Zbl0065.26103MR17,345d
- [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. Zbl0403.57002MR80b:57034
- [15] M. DAVIS and W. C. HSIANG, Concordance classes of Un and Spn actions on homotopy spheres, Ann. of Math., 105 (1977), 325-341. Zbl0345.57018MR55 #11282
- [16] M. DAVIS, W. C. HSIANG, and J. MORGAN, Concordance classes of regular O(n)-actions on homotopy spheres, to appear. Zbl0453.57026
- [17] J. DIEUDONNÉ, Topics in Local Algebra, Notre Dame Mathematical Lectures, No. 10, Notre Dame, University of Notre Dame Press (1967). Zbl0193.00101MR39 #2748
- [18] J. DIEUDONNÉ and J. CARRELL, Invariant Theory, Old and New, New York, Academic Press (1971). Zbl0196.05802MR43 #4828
- [19] E. B. DYNKIN, Semisimple subalgebras of semisimple Lie algebras, Amer. Math. Soc. Transl., 6 (1957), 111-244. Zbl0077.03404
- [20] E. B. DYNKIN, Maximal subgroups of the classical groups, Amer. Math. Soc. Transl., 6 (1957), 245-378. Zbl0077.03403
- [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. Zbl0252.22015MR46 #3689
- [22] A. G. ELASHVILI, Stationary subalgebras of points of the common state for irreducible linear Lie groups, Functional Anal. Appl., 6 (1972), 139-148. Zbl0252.22016
- [23] D. ERLE and W. C. HSIANG, On certain unitary and symplectic actions with three orbit types, Amer. J. Math., 94 (1972), 289-308. Zbl0239.57021MR46 #4558
- [24] G. GLAESER, Racine carrée d'une fonction différentiable, Ann. Inst. Fourier, 13 (1963), 203-210. Zbl0128.27903MR29 #1294
- [25] M. GOLUBITSKY and V. GUILLEMIN, Stable Mappings and Their Singularities, Graduate Texts in Mathematics, 14, New York, Springer-Verlag, 1973. Zbl0294.58004MR49 #6269
- [26] H. GRAUERT, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460-472. Zbl0108.07804MR20 #5299
- [27] A. GROTHENDIECK, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., 16 (1955). Zbl0064.35501MR17,763c
- [28] A. GROTHENDIECK, Cohomologie Locale des Faisceaux Cohérents et Théorèmes de Lefschetz Locaux et Globaux (SGA 2), Amsterdam, North-Holland (1968). Zbl0197.47202MR57 #16294
- [29] A. GROTHENDIECK, Local Cohomology (Notes by R. Hartshorne), Lecture Notes in Mathematics, No. 41, New York, Springer-Verlag (1967). Zbl0185.49202MR37 #219
- [30] R. C. GUNNING and H. ROSSI, Analytic Functions of Several Complex Variables, Englewood Cliffs, Prentice-Hall (1965). Zbl0141.08601MR31 #4927
- [31] G. HOCHSCHILD, The Structure of Lie Groups, San Francisco, Holden-Day (1965). Zbl0131.02702MR34 #7696
- [32] G. HOCHSCHILD and G. D. MOSTOW, Representations and representative functions on Lie groups III, Ann. of Math., 70 (1957), 85-100. Zbl0111.03201MR25 #5130
- [33] M. HOCHSTER, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math., 96 (1972), 318-337. Zbl0237.14019MR46 #3511
- [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. Zbl0244.13012MR46 #1787
- [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. Zbl0289.14010MR50 #311
- [36] W. C. HSIANG and W. Y. HSIANG, Differentiable actions of compact connected classical groups : I, Amer. J. Math., 89 (1967), 705-786. Zbl0184.27204MR36 #304
- [37] W. C. HSIANG, Differentiable actions of compact connected classical groups : II, Ann. of Math., 92 (1970), 189-223. Zbl0205.53902MR42 #420
- [38] W. Y. HSIANG, On the principal orbit type and P. A. Smith theory of SU (p) actions, Topology, 6 (1967), 125-135. Zbl0166.19303MR34 #5084
- [39] J. E. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, 9, New York, Springer-Verlag (1972). Zbl0254.17004MR48 #2197
- [40] J. E. HUMPHREYS, Linear Algebraic Groups, Graduate Texts in Mathematics, 21, New York, Springer-Verlag (1975). Zbl0325.20039MR53 #633
- [41] K. JÄNICH, Differenzierbare Mannigfaltigkeiten mit Rand als Orbiträume differenzierbarer G-Mannigfaltigkeiten ohne Rand, Topology, 5 (1966), 301-320. Zbl0153.53703
- [42] K. JÄNICH, On the classification of O(n)-manifolds, Math. Ann., 176 (1968), 53-76. Zbl0153.53801MR37 #2261
- [43] B. KOSTANT, Lie group representations on polynomial rings, Amer. J. Math., 85 (1963), 327-402. Zbl0124.26802MR28 #1252
- [44] M. KRÄMER, Eine Klassifikation bestimmter Untergruppen kompakter zusammenhängender Liegruppen, Comm. in Alg., 3 (1975), 691-737. Zbl0309.22013
- [45] M. KRÄMER, Some tips on the decomposition of tensor product representations of compact connected Lie groups, to appear in Reports on Mathematical Physics. Zbl0392.22007
- [46] S. LANG, Algebra, Reading, Addison-Wesley (1965). Zbl0193.34701MR33 #5416
- [47] J. A. LESLIE, On a differentiable structure for the group of diffeomorphisms, Topology, 6 (1967), 263-271. Zbl0147.23601MR35 #1041
- [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. Zbl0249.14016MR45 #3421
- [50] D. LUNA, Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105. Zbl0286.14014MR49 #7269
- [51] D. LUNA, Adhérences d'orbite et invariants, Invent. Math., 29 (1975), 231-238. Zbl0315.14018MR51 #12879
- [52] D. LUNA, Fonctions différentiables invariantes sous l'opération d'un groupe réductif, Ann. Inst. Fourier, 26 (1976), 33-49. Zbl0315.20039MR54 #11377
- [53] B. MALGRANGE, Division des distributions, Séminaire L. Schwartz (1959-1960), exposés 21-25.
- [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. Zbl0286.58003MR51 #4306
- [56] J. N. MATHER, Differentiable invariants, Topology, 16 (1977), 145-155. Zbl0376.58002MR55 #9152
- [57] G. D. MOSTOW, Self-adjoint groups, Ann. of Math., 62 (1955), 44-55. Zbl0065.01404MR16,1088a
- [58] D. MUMFORD, Geometric Invariant Theory, Erg. der Math., Bd 34, New York, Springer-Verlag (1965). Zbl0147.39304MR35 #5451
- [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). Zbl0168.06003MR36 #428
- [61] R. S. PALAIS, The classification of G-spaces, Mem. Amer. Math. Soc., No. 36 (1960). Zbl0119.38403MR31 #1664
- [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. MR22 #7129
- [63] R. RICHARDSON, Principal orbit types for algebraic transformation spaces in characteristic zero, Invent. Math., 16 (1972), 6-14. Zbl0242.14010MR45 #3405
- [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. Zbl0355.58005MR56 #3866
- [65] M. SCHLESSINGER, Rigidity of quotient singularities, Invent. Math., 14 (1971), 17-26. Zbl0232.14005MR45 #1912
- [66] G. SCHWARZ, Smooth functions invariant under the action of a compact Lie group, Topology, 14 (1975), 63-68. Zbl0297.57015MR51 #6870
- [67] G. SCHWARZ, Representations of simple Lie groups with regular rings of invariants, Invent. Math., 49 (1978), 167-191. Zbl0391.20032MR80m:14032
- [68] G. SCHWARZ, Representations of simple Lie groups with a free module of covariants, Invent. Math., 50 (1978), 1-12. Zbl0391.20033MR80c:14008
- [69] A. SEIDENBERG, A new decision method for elementary algebra, Ann. of Math., 60 (1954), 365-374. Zbl0056.01804MR16,209a
- [70] J.-P. SERRE, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, 6 (1955-1956), 1-42. Zbl0075.30401MR18,511a
- [71] J.-P. SERRE, Algèbre Locale. Multiplicités, Lecture Notes in Mathematics, No. 11, New York, Springer-Verlag (1965). Zbl0142.28603MR34 #1352
- [72] Y. T. SIU, Techniques of Extension of Analytic Objects, Lecture Notes in Pure and Applied Mathematics, No. 8, New York, Marcel Dekker (1974). Zbl0294.32007MR50 #13600
- [73] J.-CL. TOUGERON, Idéaux de Fonctions Différentiables, Erg. der Math., Bd 71, New York, Springer-Verlag (1972). Zbl0251.58001MR55 #13472
- [74] D. VOGT, Charakterisierung der Unterräume von s, Math. Z., 155 (1977), 109-117. Zbl0337.46015MR57 #3823
- [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. Zbl0373.46016MR58 #30009
- [76] D. VOGT and M. WAGNER, Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau, to appear. Zbl0464.46010
- [77] TH. VUST, Covariants de groupes algébriques réductifs, thèse, Univ. de Genève (1974). Zbl0276.14017
- [78] TH. VUST, Opération de groupes réductifs dans un type de cônes presque homogènes, Bull. Soc. Math. France, 102 (1974), 317-334. Zbl0332.22018MR51 #3187
- [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. Zbl1024.20502
- [81] H. WHITNEY, Complex Analytic Varieties, Reading, Addison-Wesley (1972). Zbl0265.32008MR52 #8473
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