zbMATH — the first resource for mathematics

Minimal models of oriented Grassmannians and applications. (English) Zbl 0986.57018
The authors give an explicit description of the minimal model of the Grassmann manifold of oriented \(k\)-dimensional vector subspaces in \(\mathbb R^n\). Several applications are given. For example, using their main result, the authors obtain an alternative proof of a classification of nilpotent real flag manifolds (consisting of unoriented flags) due to H. Glover and W. Homer [Indiana Univ. Math. J. 28, 953-956 (1979; Zbl 0398.57025)].
57N65 Algebraic topology of manifolds
55P62 Rational homotopy theory
Full Text: EuDML
[1] ALLDAY C.-PUPPE V.: Cohomological Methods in Transformation Groups. Cambridge Stud. Adv. Math. 32, Cambridge Univ. Press, Cambridge, 1993. · Zbl 0799.55001
[2] BOREL A.: Sur la cohomologie des espaces principaux et des espace homogènes de groups de Lie compacts. Ann. of Math. (2) 57 (1953), 115-207. · Zbl 0052.40001
[3] BOTT R.-TU L.: Differential Forms in Algebraic Topology. Grad. Texts in Math. 82, Springer-Verlag, New York, 1982. · Zbl 0496.55001
[4] BOUSFIELD A. K.-GUGENHEIM V. K. A. M.: On PL de Rham theory and rational homotopy type. Mem. Amer. Math. Soc. 179 (1976). · Zbl 0338.55008
[5] DELIGNE P.-GRIFFITHS P.-MORGAN J.-SULLIVAN D.: Real homotopy theory of Kähler manifolds. Invent. Math. 29 (1975), 245-274. · Zbl 0312.55011
[6] GLOVER H., HOMER W.: Equivariant immersions of flag manifolds. Indiana Univ. Math. J. 28 (1979), 953-956. · Zbl 0398.57025
[7] GREUB W.-HALPERIN S.-VANSTONE R.: Connections, Curvature, and Cohomology, Vol. III. Academic Press, New York, 1976. · Zbl 0372.57001
[8] GRIFFITHS P.-MORGAN J.: Rational Homotopy Theory and Differential Forms. Birkhäuser, Basel, 1981. · Zbl 0474.55001
[9] HELGASON S.: Differential Geometry, Lie Groups, and Symmetic Spaces. Academic Press, New York, 1978. · Zbl 0451.53038
[10] HILTON P.: Nilpotente Gruppen und nilpotente Raume. Lecture Notes in Math. 1053, Springer Verlag, New York, 1986.
[11] LANG S.: Algebra. (3rd, Addison-Wesley, Reading, Mass., 1993. · Zbl 0848.13001
[12] MILNOR J.-STASHEFF J.: Characteristic Classes. Ann. of Math. Stud. 76, Princeton Univ Press, Princeton, NJ, 1974. · Zbl 0298.57008
[13] ROITBERG J.: Note on nilpotent spaces and localization. Math. Z. 137 (1974), 67-74. · Zbl 0283.55007
[14] SPANIER E.: Algebraic Topology. Springer-Verlag, New York, 1979. · Zbl 0145.43303
[15] SULLIVAN D.: Infinitesimal computations in topology. Publ. Math., Inst. Hautes Etud. Sci. 47 (1977), 269-331. · Zbl 0374.57002
[16] TRALLE A.-OPREA J.: Symplectic Manifolds with no Kähler Structure. Lecture Notes in Math. 1661, Springer Verlag, New York. · Zbl 0891.53001
[17] VARADARAJAN K.: Nilpotent actions and nilpotent spaces. 1976
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.