REFERENCES. L. Auslander, An exposition of the structure of solvmanifolds, Bull. Amer. Math. Soc. 79 (1973),

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1 REFERENCES [A] J. F. Adams, Lectures on Lie Groups, Benjamin, New York, [Ab] E. Abbena, An example of an almost Kahler manifold which is not Kahler, Bolletino U.M.1. 3-A(6) (1984), [ABCKT] J. Amoros, M. Burger, K. Corlette, D. Kotschick and D. Toledo, Fundamental Groups of Compact Kahler Manifolds, AMS Math. Surveys and Monographs, vol. 44, Amer. Math. Soc., [ABKLR] B. Aebischer, M. Borer, M. Kalin, Ch. Leuenberger and H. M. Reimann, Symplectic Geometry, Progress in Math., vol. 124, Birkhauser, [AGH] [An] [Ar] [AT1] [AT2] [ANT] [Au1] [Au2] [AuL] [Aus] [AuSz] [Ba] [Bi] [Bch] [BGu] L. Auslander, L. Green and F. Hahn, Flows on Homogeneous Manifolds, Princeton University Press, W. Andrzejewski, Fat Bundles and Sullivan's Formality, in Polish, Ph.D. Thesis, Wroclaw, V. 1. Arnol'd, Mathematical Methods of Classical Mechanics, Grad. Texts in Math., vol. 60 2nd Ed., W. Andrzejewski and A. Tralle, Cohomology of some graded differential algebras, Fundamenta Math. 145 (1994), W. Andrzejewski and A. Tralle, Fat bundles and formality, Semin. Gaston Darboux de Geometrie et Topologie Differentielle (Montpellier) (1994), W. Andrzejewski, A. Neugebauer and A. Tralle, Rational homotopy obstructions and symplectic mechanics of a classical particle in the presence of a Yang-Mills field, Collection: Symmetry and Structural Properties of Condensed Matter" World Scientific, Singapore, 1995, pp M. Audin, The Topology of Torus Actions on Symplectic manifolds, Birkhauser, Basel, M. Audin, Exemples de uari eies presque complexes, Enseign. Math. 39 (1993), Holomorphic Curves in Symplectic Geometry (M. Audin and J. Lafontaine, eds.), Birkhauser, Basel, L. Auslander, An exposition of the structure of solvmanifolds, Bull. Amer. Math. Soc. 79 (1973), L. Auslander and R. Szczarba, Characteristic classes of compact solvmanifolds, Annals of Math. 76 (1962), 1-8. J. Barge, Structures differentielles sur les types d 'homotopie rationelle simplement connexes, Ann. Sci. Ecole Norm. Super. 9 (1976), l. G. D. Birkhoff', Proof of Poincare's geometric theorem, Trans. Amer. Math. Soc. 14 (1913), T. Bouche, La cohomologie coeffective d 'une uariet«symplectique, Bull. Sci. Math. 114 (1990), A.K. Bousfield and V.K.A.M. Guggenheim, On PL de Rham theory and rational homotopy type, Memoirs Amer. Math. Soc. 8 (179) (1976).

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7 INDEX Arnol'd conjecture 182 averaging operator 137 Benson-Gordon conjecture 70 Birkhoff's twist theorem 182 blow-up, classical 121 blow-up, along a submanifold 124 blow-up projection 124 Borel subalgebra 141 Brylinski conjecture 174 bundle, universal over cpn 120 category k-dca 1 of Lusternik-Schnirelmann (LS cat) 183 of a map 184 rational 186 Chevalley-Eilenberg complex 46 coeffective cohomology 180 differential algebra augmented 2 bigraded 190 Cartan 153 cohomologically symplectic 25 commutative graded 1 c-connected 2 a-degenerate 191 Dolbeault formal 191 elliptic 43 freely generated 2 Lefschetz 25 mimimal model 2 minimal formal 18 pure 170 of rational polynomial forms ApL 5 strictly formal 191 Sullivan-de Rham 5 Weil 154 divisor, exceptional 121 ddc-iemma 24 differential form Lee 66 symplectically harmonic 174 Dolbeault homotopy theory 190 fat bundle fat connection 161 fibration, quasi-nilpotent 7 formality criterion 18 formalizing tendency (of symplectic structures) 147 generic example of a non-formal algebra 43 g-module, triangular 83 Goldberg's conjecture 196 Hamiltonian diffeomorphism 182 Hamiltonian C-action 162 Heisenberg group 46 Hirsch extension 10 Hirzebruch surface 168 homotopy (between DCA-maps) 9 Koszul complex 155 Koszul differential 174 KS-extension 28 lattice 45 Lefschetz element 25 Leray-Serre spectral sequence 80 lifting problem 11 Lie algebra, completely solvable 77 Liouville form 22 Lupton-Oprea conjecture 147 Malcev basis 48 Massey product triple 41 quadruple 42 of higher order 42

8 INDEX manifold CFG-manifold 56 cosymplectic 181 contact 61 Dobeault formal 191 formal 18 generalized Heisenberg 46 generalized Hopf 66 Kahler 23 Kodaira-Thurston.53 locally conformal Kahler 66 parallelizable 68 strictly formal 183 symplectic 21 model, cofibrant 181 model, of a DGA-map 13 moment map 15.5 Mostow bundle 71 Mostow structure theorem 71 nilmanifold 45 nilpotent action (of a group) 6 P-algebra 154 P-algebra, symmetric 1.58 parabolic subalgebra 141 Poincare's Last Geometric Theorem 173 problem of Thurston-Weinstein 26 quasi-isomorphism 2 regular element (of a Lie group) 72 regular sequence (in a ring) 157 representation (of a Lie algebra), triangular rigidity theorem 73 Sullivan's algorithm 158 Sullivan's problem 199 Samelson projection 156 Samelson subspace 156 Toomer's invariant 186 topological space, nilpotent 6 sl(2)-representation, of finite H -spectrum 178 solvmanifold 71 symplectic quotient 198 symplectic star operator 174 Theorem (of) Benson-Gordon 116 Benson-Gordon-Hasegawa 54 H. Cartan 153 Chevalley 152 Darboux 21 Deligne-Griffiths-Morgan- Sullivan 24 fundamental, of rational homotopy theory 6 Hattori 77 Nomizu 46 P.L. de Rham 5 Thurston's conjecture 199 truncated de Rham cohomology group 180 twisted tensor product 111 Wang's theorem 166 Weinstein's problem (for fiber bundles) 140

Citation Osaka Journal of Mathematics. 43(1)

TitleA note on compact solvmanifolds wit Author(s) Hasegawa, Keizo Citation Osaka Journal of Mathematics. 43(1) Issue 2006-03 Date Text Version publisher URL http://hdl.handle.net/11094/11990 DOI Rights