Harmonic cohomology of symplectic manifolds

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

Mathieu (Math. Helv. 70 (1995) 1) introduced a canonic filtration in the de Rham cohomology of a symplectic manifold and proved, that the middle filtration space is the space of harmonic cohomology classes. We give an interpretation of the other filtration spaces, prove a Kušnneth theorem for harmonic cohomology, prove PoincareŽ duality for harmonic cohomology and show how surjectivity of certain Lefschetz type mappings is related to properties of the filtration. For a closed symplectic manifold M we also introduce symplectic invariants sl (M), l=0, and show ?l=0 sl (M) = sign(M) if M is of dimension 2n with n even. Œ 2003 Elsevier Science (USA). All rights reserved.
OriginalspracheEnglisch
Seiten (von - bis)87-103
Seitenumfang17
FachzeitschriftAdvances in Mathematics
Jahrgang180
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 2003

ÖFOS 2012

  • 1010 Mathematik

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