Compact fiberings of homogeneous spaces. I
Compositio Mathematica (1981)
- Volume: 43, Issue: 2, page 181-215
- ISSN: 0010-437X
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topSchultz, Reinhard. "Compact fiberings of homogeneous spaces. I." Compositio Mathematica 43.2 (1981): 181-215. <http://eudml.org/doc/89496>.
@article{Schultz1981,
author = {Schultz, Reinhard},
journal = {Compositio Mathematica},
keywords = {homogeneous spaces; compact fibering of a finite complex; reduced flag manifold; quotients of compact Lie groups by maximal closed subgroups; quaternionic projective spaces; Grassmann manifolds of 2-planes in complex or quaternionic n-space; Grassmann manifolds of 2-planes in real n-space; fibre space transfer; rational fibrations and minimal models},
language = {eng},
number = {2},
pages = {181-215},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Compact fiberings of homogeneous spaces. I},
url = {http://eudml.org/doc/89496},
volume = {43},
year = {1981},
}
TY - JOUR
AU - Schultz, Reinhard
TI - Compact fiberings of homogeneous spaces. I
JO - Compositio Mathematica
PY - 1981
PB - Sijthoff et Noordhoff International Publishers
VL - 43
IS - 2
SP - 181
EP - 215
LA - eng
KW - homogeneous spaces; compact fibering of a finite complex; reduced flag manifold; quotients of compact Lie groups by maximal closed subgroups; quaternionic projective spaces; Grassmann manifolds of 2-planes in complex or quaternionic n-space; Grassmann manifolds of 2-planes in real n-space; fibre space transfer; rational fibrations and minimal models
UR - http://eudml.org/doc/89496
ER -
References
top- [1] L.V. Ahlfors: Lectures on Quasiconformal Mappings. Van Nostrand Mathematical Studies No. 10. Van NostrandReinhold, Princeton, 1966. Zbl0138.06002MR200442
- [2] J.C. Becker and D.H. Gottlieb: Applications of the evaluation map and transfer map theorems. Math. Ann.211 (1974) 277-288. Zbl0275.55027MR358772
- [3] J.C. Becker and D.H. Gottlieb: Transfer maps for fibrations and duality. Comp. Math.33 (1976) 107-133. Zbl0354.55009MR436137
- [4] C.T. Benson and L.C. Grove: Finite Reflection Groups. Bogden and Quigley, Tarrytown, N.Y., 1971. MR383218
- [5] A. Borel: Le plan projectif des octaves et les sphères comme espaces homogènes. C.R. Acad. Sci. Paris230 (1950) 1378-1380. Zbl0041.52203MR34768
- [6] A. Borel (ed.): Seminar on Transformation Groups. Ann. of Math. Studies No. 46. Princeton University Press, Princeton, 1960. Zbl0091.37202MR116341
- [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. Zbl0034.30701MR32659
- [8] G. Bredon: Introduction to Compact Transformation Groups. Pure and Appl. Math. Vol. 46. Academic Press, New York, 1972. Zbl0246.57017MR413144
- [9] G. Bredon: Fixed point sets of actions on Poincaré duality spaces. Topology12 (1973) 159-175. Zbl0253.57005MR331375
- [10] S. Brewster: Automorphisms of the cohomology ring of finite Grassmann manifolds. Ph.D. Thesis, OhioState University, 1978.
- [11] W. Browder: Higher torsion in H-spaces. Trans. Amer. Math. Soc.108 (1963) 353-375. Zbl0114.14404MR155326
- [12] A. Casson and D.H. Gottlieb: Fibrations with compact fibres. Amer. J. Math.99 (1977) 159-189. Zbl0375.55015MR436144
- [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. Zbl0083.17801MR87943
- [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. Zbl0077.03403MR49903
- [15] A.L. Edmonds: Fibering topological manifolds. Proc. AMS Sympos. Pure Math.32, Pt. 2, 13-18. American Mathematical Society, Providence, 1978. Zbl0394.55011MR520519
- [16] C. Ehresmann: Sur les espaces différentiables fibrés. C.R. Acad. Sci. Paris224 (1947) 1611-1612. Zbl0029.42001MR20774
- [17] E. Fadell: Recent results in the fixed point theory of continuous maps. Bull. Amer. Math. Soc.76 (1970) 10-29. Zbl0206.25003MR271935
- [18] B. Friberg: A topological proof of a theorem of Kneser. Proc. Amer. Math. Soc.39 (1973) 421-427. Zbl0273.57017MR321124
- [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. Zbl0385.57011MR513548
- [20] D.H. Gottlieb: A certain subgroup of the fundamental group. Amer. J. Math.87 (1965) 840-856. Zbl0148.17106MR189027
- [21] D.H. Gottlieb: On fibre spaces and the evaluation map. Ann. of Math.87 (1968) 42-55.Correction, 91 (1970) 640-642. Zbl0199.26601MR221508
- [22] D.H. Gottlieb: Evaluation subgroups of homotopy groups. Amer. J. Math.91 (1969) 729-756. Zbl0185.27102MR275424
- [23] D.H. Gottlieb: Fibering suspensions. Houston J. Math.4 (1978) 49-65. Zbl0382.55007MR482759
- [24] D.H. Gottlieb.Poincaré duality and fibrations. Proc. Amer. Math. Soc.76 (1979) 148-150. Zbl0423.57009MR534407
- [25] S. Halperin: Finiteness in the minimal models of Sullivan. Trans. Amer. Math. Soc.230 (1977) 173-199. Zbl0364.55014MR461508
- [26] S. Halperin: Rational fibrations, minimal models, and fiberings of homogeneous spaces. Trans. Amer. Math. Soc.244 (1978) 199-224. Zbl0387.55010MR515558
- [27] G.H. Hardy and E.M. Wright: Introduction to the Theory of Numbers (Fourth Ed.). Oxford Univ. Press, New York, 1960. Zbl0086.25803MR67125
- [28] F. Hirzebruch: Topological Methods in Algebraic Geometry, Grundlehren der Mathematischen Wissenschaften Bd. 131. Springer, New York, 1966. MR202713
- [29] W.V.D. Hodge and D. Pedoe: Methods of Algebraic Geometry II. Cambridge University Press, New York, 1952. Zbl0796.14003MR48065
- [30] H. Hopf and H. Samelson: Ein Satz über die Wirkungsräume geschloßener Liescher Gruppen. Comment. Math. Helv.13 (1941) 240-251. Zbl0025.23704MR6546JFM67.0749.01
- [31] W.-C. Hsiang and W.-Y. Hsiang: Differentiable actions of compact connected classical groups. II. Ann. of Math.92 (1970) 189-223. Zbl0205.53902MR265511
- [32] N. Jacobson: Lie Algebras. Interscience Tracts in Pure and Appl. Math. Vol. 10. Wiley-Interscience, New York, 1960. Zbl0121.27504MR143793
- [33] N. Jacobson: Exceptional Lie Algebras, Lecture Notes in Pure and Applied Math. No. 1. Marcel Dekker, New York, 1971. Zbl0215.38701MR284482
- [34] M. Krämer: Hauptisotropiegruppen bei endlich dimensionalen Darstellungen kompakter halbeinfacher Liegruppen. Diplomarbeit, Mathematisches Institut der UniversitätBonn, 1966.
- [35] H.F. Lai: On the topology of even-dimensional complex quadrics. Proc. Amer. Math. Soc.46 (1974) 419-425. Zbl0264.57005MR358846
- [36] K.Y. Lam: A formula for the tangent bundles of flag manifolds and related manifolds. Trans. Amer. Math. Soc.213 (1975) 305-314. Zbl0312.55020MR431194
- [37] W.J. Leveque: Topics in Number Theory, Vol. I. Addison-Wesley, Reading, Mass., 1956. Zbl0070.03803MR80682
- [38] C.B. De Lyra: On the homotopy type of a factor space. An. Acad. Brasil Ci.30 (1958) 37-41. Zbl0090.13001MR97799
- [39] J. Milnor: Groups which act freely on Sn without fixed points. Amer. J. Math.79 (1957) 623-630. Zbl0078.16304MR90056
- [40] L.S. O'Neill: The fixed point property for Grassmann manifolds. Ph.D. Thesis, OhioState University, 1974.
- [41] A.V. Phillips: Submersions of open manifolds. Topology6 (1967) 171-206. Zbl0204.23701MR208611
- [42] F.S. Quinn: Surgery on Poincaré and normal spaces. Bull. Amer. Math. Soc.78 (1972) 262-267. Zbl0233.57007MR296955
- [43] J.-P. Serre: Groupes d'homotopie et classes de groupes abélien. Ann. of Math.58 (1953) 258-294. Zbl0052.19303MR59548
- [44] L.C. Siebenmann: Deformations of homeomorphisms of stratified sets. Comment. Math. Helv.47 (1972) 123-163. Zbl0252.57012MR319207
- [45] E.H. Spanier: Algebraic Topology. McGraw-Hill, New York, 1967. Zbl0145.43303MR210112
- [46] N.E. Steenrod: The Topology of Fibre Bundles, Princeton Mathematical Series No. 14. Princeton University Press, Princeton, 1951. Zbl0054.07103MR39258
- [47] N.E. STEENROD (ed.): Reviews of Papers in Algebraic and Differential Topology, Topological Groups, and Homological Algebra. American Mathematical Society, Providence, 1968. Zbl0172.24903MR235549
- [48] N. Steenrod and D.B.A. Epstein: Cohomology Operations. Ann. of Math. Studies No. 50.Princeton University Press, Princeton, 1962. Zbl0102.38104MR145525
- [49] C.T.C. Wall: Poincaré complexes. Ann. of Math.86 (1967) 213-245. Zbl0153.25401MR217791
- [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. Zbl0375.57013MR451247
- [51] J.A. Wolf: Spaces of Constant Curvature. (Fourth Edition). Publish or Perish, Berkeley, California, 1977. MR928600
- [52] G.S. Young: A characterization of 2-manifolds. Duke Math. J.14 (1947) 979-990. Zbl0029.23204MR23061
- [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. MR492946
- [54] A. Stieglitz: Poincaré duality of fibre maps, (preprint) Universität Bochum, 1980.
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