Abstract.
In the present paper we study the variation of the dimensions h k of spaces of symplectically harmonic cohomology classes (in the sense of Brylinski) on closed symplectic manifolds. We give a description of such variation for all 6-dimensional nilmanifolds equipped with symplectic forms. In particular, it turns out that certain 6-dimensional nilmanifolds possess families of homogeneous symplectic forms \( \omega_t \) for which numbers \( h_k({\rm M},\omega_t) \) vary with respect to t. This gives an affirmative answer to a question raised by Boris Khesin and Dusa McDuff. Our result is in contrast with the case of 4-dimensional nilmanifolds which do not admit such variations by a remark of Dong Yan.
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Received: March 24, 2000
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Ibáñez, R., Rudyak, Y., Tralle, A. et al. On symplectically harmonic forms on six-dimensional nilmanifolds. Comment. Math. Helv. 76, 89–109 (2001). https://doi.org/10.1007/s000140050151
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DOI: https://doi.org/10.1007/s000140050151