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Formality and the Lefschetz property in symplectic and cosymplectic geometry

100%

Bazzoni G., Fernández M., Muñoz V.

Complex Manifolds

2015

tom 2

nr 1

We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).

The geometry of a closed form

100%

Fernández M., Ibáñez R., de León M.

Banach Center Publications

1998

tom 45

nr 1

155-167

It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on $G_{2}$-manifolds and fundamental 4-forms in quaternionic manifolds are discussed.

Ograniczanie wyników

1 Banach Center Publications

1 Complex Manifolds

2 Fernández M.

1 Bazzoni G.

1 Ibáñez R.

1 Muñoz V.

1 de León M.

1 2015

1 1998

Wyniki wyszukiwania

Formality and the Lefschetz property in symplectic and cosymplectic geometry

The geometry of a closed form