Symplectic cohomologies and deformations

  • Nicoletta Tardini
  • Adriano TomassiniEmail author


In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-Kähler manifolds \((X,J,g,\omega )\) with J\({\mathcal {C}}^\infty \)-pure and full the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. Furthermore, we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms.


Symplectic deformation Symplectic structure Cohomology 

Mathematics Subject Classification

32Q60 53C15 58A12 53D05 


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Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di FirenzeFirenzeItaly
  2. 2.Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Unità di Matematica e InformaticaUniversità di ParmaParmaItaly

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