Compact fiberings of homogeneous spaces. I

Schultz, Reinhard

Schultz, Reinhard

Compositio Mathematica, Tome 43 (1981) no. 2, pp. 181-215.

corrigé par Correction to the paper “Compact fiberings of homogeneous spaces. I”

MR Zbl | 1 citation dans Numdam

@article{CM_1981__43_2_181_0,
     author = {Schultz, Reinhard},
     title = {Compact fiberings of homogeneous spaces. {I}},
     journal = {Compositio Mathematica},
     pages = {181--215},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {43},
     number = {2},
     year = {1981},
     mrnumber = {622447},
     zbl = {0479.55011},
     language = {en},
     url = {http://www.numdam.org/item/CM_1981__43_2_181_0/}
}

TY  - JOUR
AU  - Schultz, Reinhard
TI  - Compact fiberings of homogeneous spaces. I
JO  - Compositio Mathematica
PY  - 1981
SP  - 181
EP  - 215
VL  - 43
IS  - 2
PB  - Sijthoff et Noordhoff International Publishers
UR  - http://www.numdam.org/item/CM_1981__43_2_181_0/
LA  - en
ID  - CM_1981__43_2_181_0
ER  -

%0 Journal Article
%A Schultz, Reinhard
%T Compact fiberings of homogeneous spaces. I
%J Compositio Mathematica
%D 1981
%P 181-215
%V 43
%N 2
%I Sijthoff et Noordhoff International Publishers
%U http://www.numdam.org/item/CM_1981__43_2_181_0/
%G en
%F CM_1981__43_2_181_0

Schultz, Reinhard. Compact fiberings of homogeneous spaces. I. Compositio Mathematica, Tome 43 (1981) no. 2, pp. 181-215. http://www.numdam.org/item/CM_1981__43_2_181_0/

Bibliographie
Cité par

[1] L.V. Ahlfors: Lectures on Quasiconformal Mappings. Van Nostrand Mathematical Studies No. 10. Van Nostrand Reinhold, Princeton, 1966. | MR | Zbl

[2] J.C. Becker and D.H. Gottlieb: Applications of the evaluation map and transfer map theorems. Math. Ann. 211 (1974) 277-288. | MR | Zbl

[3] J.C. Becker and D.H. Gottlieb: Transfer maps for fibrations and duality. Comp. Math. 33 (1976) 107-133. | Numdam | MR | Zbl

[4] C.T. Benson and L.C. Grove: Finite Reflection Groups. Bogden and Quigley, Tarrytown, N.Y., 1971. | MR

[5] A. Borel: Le plan projectif des octaves et les sphères comme espaces homogènes. C.R. Acad. Sci. Paris 230 (1950) 1378-1380. | MR | Zbl

[6] A. Borel (ed.): Seminar on Transformation Groups. Ann. of Math. Studies No. 46. Princeton University Press, Princeton, 1960. | MR | Zbl

[7] A. Borel and J. De Siebenthal: Les sous-groupes fermés de rang maximum des groupes de Lie clos. Comment. Math. Helv. 23 (1949) 200-221. | MR | Zbl

[8] G. Bredon: Introduction to Compact Transformation Groups. Pure and Appl. Math. Vol. 46. Academic Press, New York, 1972. | MR | Zbl

[9] G. Bredon: Fixed point sets of actions on Poincaré duality spaces. Topology 12 (1973) 159-175. | MR | Zbl

[10] S. Brewster: Automorphisms of the cohomology ring of finite Grassmann manifolds. Ph.D. Thesis, Ohio State University, 1978.

[11] W. Browder: Higher torsion in H-spaces. Trans. Amer. Math. Soc. 108 (1963) 353-375. | MR | Zbl

[12] A. Casson and D.H. Gottlieb: Fibrations with compact fibres. Amer. J. Math. 99 (1977) 159-189. | MR | Zbl

[13] S.S. Chern, F. Hirzebruch, and J.-P. Serre: On the index of a fibered manifold. Proc. Amer. Math. Soc. 8 (1957) 587-596. | MR | Zbl

[14] E.B. Dynkin: Maximal subgroups of the classical groups (Russian). Trudy Moskov. Mat. Obšč. 1 (1952) 39-166; English transl., A.M.S. Translations (2) 6 (1957) 245-378. | MR | Zbl

[15] A.L. Edmonds: Fibering topological manifolds. Proc. AMS Sympos. Pure Math. 32, Pt. 2, 13-18. American Mathematical Society, Providence, 1978. | MR | Zbl

[16] C. Ehresmann: Sur les espaces différentiables fibrés. C.R. Acad. Sci. Paris 224 (1947) 1611-1612. | MR | Zbl

[17] E. Fadell: Recent results in the fixed point theory of continuous maps. Bull. Amer. Math. Soc. 76 (1970) 10-29. | MR | Zbl

[18] B. Friberg: A topological proof of a theorem of Kneser. Proc. Amer. Math. Soc. 39 (1973) 421-427. | MR | Zbl

[19] H. Glover and W. Homer: Endomorphisms of the cohomology ring of finite Grassmann manifolds, Geometric Applications of Homotopy Theory I (Proceedings, Evanston, 1977). Lecture Notes in Math. Vol. 657, 170-193. Springer, New York, 1978. | MR | Zbl

[20] D.H. Gottlieb: A certain subgroup of the fundamental group. Amer. J. Math. 87 (1965) 840-856. | MR | Zbl

[21] D.H. Gottlieb: On fibre spaces and the evaluation map. Ann. of Math. 87 (1968) 42-55.Correction, 91 (1970) 640-642. | MR | Zbl

[22] D.H. Gottlieb: Evaluation subgroups of homotopy groups. Amer. J. Math. 91 (1969) 729-756. | MR | Zbl

[23] D.H. Gottlieb: Fibering suspensions. Houston J. Math. 4 (1978) 49-65. | MR | Zbl

[24] D.H. Gottlieb. Poincaré duality and fibrations. Proc. Amer. Math. Soc. 76 (1979) 148-150. | MR | Zbl

[25] S. Halperin: Finiteness in the minimal models of Sullivan. Trans. Amer. Math. Soc. 230 (1977) 173-199. | MR | Zbl

[26] S. Halperin: Rational fibrations, minimal models, and fiberings of homogeneous spaces. Trans. Amer. Math. Soc. 244 (1978) 199-224. | MR | Zbl

[27] G.H. Hardy and E.M. Wright: Introduction to the Theory of Numbers (Fourth Ed.). Oxford Univ. Press, New York, 1960. | MR | Zbl

[28] F. Hirzebruch: Topological Methods in Algebraic Geometry, Grundlehren der Mathematischen Wissenschaften Bd. 131. Springer, New York, 1966. | MR

[29] W.V.D. Hodge and D. Pedoe: Methods of Algebraic Geometry II. Cambridge University Press, New York, 1952. | MR | Zbl

[30] H. Hopf and H. Samelson: Ein Satz über die Wirkungsräume geschloßener Liescher Gruppen. Comment. Math. Helv. 13 (1941) 240-251. | JFM | MR | Zbl

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

[32] N. Jacobson: Lie Algebras. Interscience Tracts in Pure and Appl. Math. Vol. 10. Wiley-Interscience, New York, 1960. | MR | Zbl

[33] N. Jacobson: Exceptional Lie Algebras, Lecture Notes in Pure and Applied Math. No. 1. Marcel Dekker, New York, 1971. | MR | Zbl

[34] M. Krämer: Hauptisotropiegruppen bei endlich dimensionalen Darstellungen kompakter halbeinfacher Liegruppen. Diplomarbeit, Mathematisches Institut der Universität Bonn, 1966.

[35] H.F. Lai: On the topology of even-dimensional complex quadrics. Proc. Amer. Math. Soc. 46 (1974) 419-425. | MR | Zbl

[36] K.Y. Lam: A formula for the tangent bundles of flag manifolds and related manifolds. Trans. Amer. Math. Soc. 213 (1975) 305-314. | MR | Zbl

[37] W.J. Leveque: Topics in Number Theory, Vol. I. Addison-Wesley, Reading, Mass., 1956. | MR | Zbl

[38] C.B. De Lyra: On the homotopy type of a factor space. An. Acad. Brasil Ci. 30 (1958) 37-41. | MR | Zbl

[39] J. Milnor: Groups which act freely on Sn without fixed points. Amer. J. Math. 79 (1957) 623-630. | MR | Zbl

[40] L.S. O'Neill: The fixed point property for Grassmann manifolds. Ph.D. Thesis, Ohio State University, 1974.

[41] A.V. Phillips: Submersions of open manifolds. Topology 6 (1967) 171-206. | MR | Zbl

[42] F.S. Quinn: Surgery on Poincaré and normal spaces. Bull. Amer. Math. Soc. 78 (1972) 262-267. | MR | Zbl

[43] J.-P. Serre: Groupes d'homotopie et classes de groupes abélien. Ann. of Math. 58 (1953) 258-294. | MR | Zbl

[44] L.C. Siebenmann: Deformations of homeomorphisms of stratified sets. Comment. Math. Helv. 47 (1972) 123-163. | MR | Zbl

[45] E.H. Spanier: Algebraic Topology. McGraw-Hill, New York, 1967. | MR | Zbl

[46] N.E. Steenrod: The Topology of Fibre Bundles, Princeton Mathematical Series No. 14. Princeton University Press, Princeton, 1951. | MR | Zbl

[47] N.E. STEENROD (ed.): Reviews of Papers in Algebraic and Differential Topology, Topological Groups, and Homological Algebra. American Mathematical Society, Providence, 1968. | MR | Zbl

[48] N. Steenrod and D.B.A. Epstein: Cohomology Operations. Ann. of Math. Studies No. 50. Princeton University Press, Princeton, 1962. | MR | Zbl

[49] C.T.C. Wall: Poincaré complexes. Ann. of Math. 86 (1967) 213-245. | MR | Zbl

[50] J.E. West: Mapping Hilbert cube manifolds to ANR's: A solution to a conjecture of Borsuk. Ann. of Math. 106 (1977) 1-18. | MR | Zbl

[51] J.A. Wolf: Spaces of Constant Curvature. (Fourth Edition). Publish or Perish, Berkeley, California, 1977. | MR

[52] G.S. Young: A characterization of 2-manifolds. Duke Math. J. 14 (1947) 979-990. | MR | Zbl

[53] C.J. Earle: Teichmüller theory, Discrete Groups and Automorphic Functions (Proc. Instr. Conf., Cambridge, U.K., 1975), 143-162. Academic Press, New York, 1977. | MR

[54] A. Stieglitz: Poincaré duality of fibre maps, (preprint) Universität Bochum, 1980.