Fernandez, MarisaMuñoz, VicenteSantisteban, José A.Bokan, NedaDjoric, MirianaFomenco, Anatoly T.Rakic, ZoranWess, Julius2023-06-202023-06-202004J. Amoros, M. Burger, K. Corlette, D. Kotschick, D. Toledo, Fundamental groups of compact Kahler manifolds, Math. Sur.and Monogr. 44, Amer. Math. Soc., 1996. D. Arapura, M. Nori, Solvable fundamental groups of algebraic varieties and Kahler manifolds,Compositio Math. 116 (1999), 173-188. D. Auroux, Asymptotically holomorphic families of symplectic submanifolds, Geom. Funct. Anal. 7 (1997), 971-995. C. Benson, C.S. Gordon, Kahler and symplectic structures on nilmanifolds, Topology 27 (1988), 513-518. F. Campana, Remarques sur les groupes de Kahler nilpotents, Ann. Scient. Ec. Norm. Sup. 28 (1995), 307-316. L.A. Cordero, M. Fernandez, A. Gray, Symplectic manifolds with no Kahler structure, Topology 25 (1986), 375-380. J.M. Dardie, A. Medina, Algµebres de Lie kahleriennes et double extension, J. Algebra 185 (1986),774-795. P. Deligne, P. Gri±ths, J. Morgan, D. Sullivan, Real homotopy theory of Kahler manifolds, Invent.Math. 29 (1975), 245-274. S.K. Donaldson, Symplectic submanifolds and almost-complex geometry, J. Dif. Geom. 44 (1996),666-705. M. Fernandez and V. Muñoz, On the formality and the hard Lefschetz property for Donaldson symplectic manifolds.Preprint 2002 math.SG/0211017. M. Fernandez, V. Muñoz and J. Santisteban, Cohomologically Kahler Manifolds with no Kahler Metrics. Preprint 2002. A. Floer, Symplectic ed points and holomorphic spheres, Commun. Math. Phys. 120 (1989),575-611. R. Gompf, A new construction of symplectic manifolds, Ann. of Math. 142 (1995), 527-597. R. Gompf, On symplectically aspherical symplectic manifolds with nontrivial π2, Math. Res. Letters 5 (1999), 599-603. P. Gri±ths, J.W. Morgan, Rational homotopy theory and differential forms, Progress in Math. 16,Birkhauser, 1981. D. Guan, Examples of compact holomorphic symplectic manifolds which are not Kahlerian II, Invent.Math. 121 (1995), 135-145. S. Halperin, Lectures on minimal models, Mem. Soc. Math. France 230, 1983. A. Hattori, Spectral sequence in the de Rham cohomology of bre bundles, J. Fac. Sci. Univ. Tokyo 8 (1960), 298-331. R. Ibañez, J. Kedra, Y. Rudyak, A. Tralle, Symplectically aspherical manifolds. Preprint 2003 math.SG/0103098. [20] D. McDuff, Examples of symplectic simply connected manifolds with no Kahler structure, J. Diff.Geom. 20 (1984), 267-277. W.P. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976),467-468. A. Tralle, J. Oprea, Symplectic manifolds with no Kahler structure, Lecture Notes in Math. 1661,Springer-Verlag,1997. A. Weinstein, Lectures on symplectic manifolds, Conference Board of the Math. Sciences, regional conference series in math. 29, Univ. North Carolina 1976, Amer. Math.Soc.Providence, Rhode Island, 1977.978-981-238-432-410.1142/9789812703088_0010https://hdl.handle.net/20.500.14352/53238In a previous paper, the authors show some examples of compact symplectic solvman-ifolds, of dimension six, which are cohomologically KÄahler and they do not admit Kahler metrics because their fundamental groups cannot be the fundamental group of any compact Kahler manifold. Here we generalize such manifolds to higher dimension and, by using Au-roux symplectic submanifolds [3], we construct four-dimensional symplectically aspherical manifolds with nontrivial ¼2 and with no Kahler metrics.engSymplectically aspherical manifolds with nontrivial π2 and with no Kähler metrics.book parthttp://www.mat.ucm.es/~vmunozve/Aspherical.pdfhttp://www.worldscientific.comopen access514symplectically aspherical manifoldsAuroux symplectic submanifoldsHomotopy groupsFormalityHard Lefschetz theoremGeometría1204 Geometría