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SYMPLECTICALLY ASPHERICAL MANIFOLDS WITH NONTRIVIAL π₂ AND WITH NO KÄHLER METRICS

Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain

Partially supported through grants MCYT (Spain) Project BFM2001-3778-c03-02 and UPV 00127.310-e-14813/2002. Also partially supported by The European Contract Human Potential Programme, Research Training Network HPRN-CT-2000-00101.

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V. MUÑOZ

Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Supported by MCYT (Spain) Project BFM2000-0024. Also partially supported by The European Contract Human Potential Programme, Research Training Network HPRN-CT-2000-00101.

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J. A. SANTISTEBAN

Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain

Partially supported through grants MCYT (Spain) Project BFM2001-3778-c03-02 and UPV 00127.310-e-14813/2002.

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https://doi.org/10.1142/9789812703088_0010Cited by:2 (Source: Crossref)

Abstract:

In a previous paper, the authors show some examples of compact symplectic solvmanifolds, of dimension six, which are cohomologically Kähler and they do not admit Kähler metrics because their fundamental groups cannot be the fundamental group of any compact Kähler manifold. Here we generalize such manifolds to higher dimension and, by using Auroux symplectic submanifolds [3], we construct four-dimensional symplectically aspherical manifolds with nontrivial π₂ and with no Kähler metrics.

Keywords:

AMSC: 53D05, 55P62