Symplectic Bott–Chern cohomology of solvmanifolds

We study the symplectic Bott–Chern cohomology by L.-S. Tseng and S.-T. Yau for solvmanifolds endowed with left-invariant symplectic structures. Our results are applicable to cohomology with values in local systems. Studying symplectic Bott–Chern cohomology of solvmanifolds with values in local systems, we give some remarks on symplectic Hodge theory.

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During the preparation of this work, the first author has been granted with a research fellowship by Istituto Nazionale di Alta Matematica INdAM and with a Junior Visiting Position at Centro di Ricerca Matematica “Ennio de Giorgi” in Pisa, and he is supported by the Project PRIN “Variet`a reali e complesse: geometria, topologia e analisi armonica”, by the Project FIRB “Geometria Differenziale e Teoria Geometrica delle Funzioni”, by project SIR 2014 AnHyC “Analytic aspects in complex and hypercomplex geometry” (code RBSI14DYEB), and by GNSAGA of INdAM. The second author is supported by JSPS Research Fellowships for Young Scientists.

Received 30 November 2015

Accepted 14 June 2018

Published 23 May 2019