Document Zbl 0517.55005

Some topological properties of Kaehler manifolds and homogeneous spaces. (English) Zbl 0517.55005

Math. Z. 183, 473-481 (1983).

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MSC:

55P62	Rational homotopy theory
55P10	Homotopy equivalences in algebraic topology
57R50	Differential topological aspects of diffeomorphisms
53C30	Differential geometry of homogeneous manifolds
58B05	Homotopy and topological questions for infinite-dimensional manifolds
55Q52	Homotopy groups of special spaces

Keywords:

homotopy groups of the space of self equivalences; homotopy self equivalences of a space; CW-complex with evenly graded rational cohomology; compact homogeneous Kaehler manifold; group of fibre homotopy self equivalences of a fibration; rational homotopy groups of diffeomorphism groups

Citations:

Zbl 0489.57008; Zbl 0414.18010; Zbl 0173.259

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Full Text: DOI EuDML

References:

[1]	Blanchard, A.: Sur les variétés analytiques complexes. Ann. Sci. Ecole Norm. Sup.73, 157-202 (1957)
[2]	Borel, A.: Kählerian coset spaces of semisimple Lie groups. Proc. Nat. Acad. Sci. USA,40, 1147-1151 (1954) · Zbl 0058.16002 · doi:10.1073/pnas.40.12.1147
[3]	Borel, A.: Seminar on Transformation groups. Ann. of Math. Studies, 46, Princeton: Princeton University Press 1960 · Zbl 0091.37202
[4]	Baum, P.: On the cohomology of homogeneous spaces. Topology7, 15-38 (1968) · Zbl 0158.42002 · doi:10.1016/0040-9383(86)90012-1
[5]	Brewster, S.: Automorphisms of the cohomology ring of finite Grassmann manifolds. Ph.D. dissertation, Ohio State University 1978
[6]	Burghelea, D.: The rational homotopy groups of Diff(M) and Homeo(M) in the stability range. In: Proceedings of a conference on Algebraic Topology (Aarhus 1978), pp. 604-626. Lecture Notes in Math.763. Berlin-Heidelberg-New York: Springer 1979
[7]	Burghelea, D., Lashof, R.: Geometric transfer and the homotopy type of the automorphism groups of manifolds. Trans. Amer. Math. Soc.269, 1-38 (1982) · Zbl 0489.57008 · doi:10.1090/S0002-9947-1982-0637027-4
[8]	Glover, H., Homer, W.: Self-Maps of Flag Manifolds. Trans. Amer. Math. Soc.267, 423-434 (1981) · Zbl 0479.55014 · doi:10.1090/S0002-9947-1981-0626481-9
[9]	Gottlieb, D.: On Fibre spaces and the evaluation map. Ann. of Math.87, 42-55 (1968) · Zbl 0173.25901 · doi:10.2307/1970593
[10]	Gottlieb, D.: Witnesses, transgressions and the evaluation map. Indiana Univ. Math. J.24, 825-836 (1975) · Zbl 0299.55007 · doi:10.1512/iumj.1975.24.24065
[11]	Griffiths, P., Harris, J.: Principles of Algebraic Geometry. New York: Wiley and Sons 1978 · Zbl 0408.14001
[12]	Halperin, S.: Finiteness in the minimal models of Sullivan. Trans. Amer. Math. Soc.230, 173-199 (1977) · Zbl 0364.55014 · doi:10.1090/S0002-9947-1977-0461508-8
[13]	Hatcher, A.: Higher simple homotopy theory. Ann. of Math.102, 101-137 (1975) · Zbl 0305.57009 · doi:10.2307/1970977
[14]	Hsiang, W., Staffeldt, R.: Rational AlgebraicK-theory of a product of Eilenberg-MacLane spaces. Preprint · Zbl 0527.55019
[15]	Liulevicius, A.: Flag Manifolds and Homotopy Rigidity of Linear Actions, In: Proceedings of a conference on Algebraic Topology (Vancouver 1977), pp. 254-261. Lecture Notes in Math.673. Berlin-Heidelberg-New York: Springer 1978
[16]	Meier, W.: Rational Universal Fibrations and Flag Manifolds. Math. Ann.258, 329-340 (1982) · doi:10.1007/BF01450686
[17]	Scheerer, H.: Arithmeticity of groups of fibre homotopy equivalence classes. Preprint · Zbl 0451.55006
[18]	Sullivan, D.: Infinitesimal computations in topology. Inst. Hautes Études Sci. Publ. Math.47, 269-331 (1978) · Zbl 0374.57002 · doi:10.1007/BF02684341
[19]	Waldhausen, F.: AlgebraicK-theory of topological spaces, I. Proc. Sympos. Pure Math.32, 35-60 (1978)

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