Abstract
In this paper, we consider decompositions of basic degree 2 cohomology for a compact K-contact 5-manifold \({(M,\xi,\eta,\Phi,g)}\), and conclude the pureness and fullness of \({\Phi}\)-invariant and \({\Phi}\)-anti-invariant cohomology groups. Moreover, we discuss the decomposition of the complexified basic degree 2 cohomology group. This is an analogue problem when Draghici et al. (Int. Math. Res. Not. IMRN 1:1–17, 2010) considered the \({C^{\infty}}\) pureness and fullness of \({J}\)-invariant and \({J}\)-anti-invariant subgroups of the degree 2 real cohomology group \({H^2(M,\mathbb{R})}\) of any compact almost complex manifold \({(M, J)}\).
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Zhou, J., Zhu, P. Basic Cohomology Group Decomposition of K-Contact 5-Manifolds. Results Math 71, 1023–1030 (2017). https://doi.org/10.1007/s00025-016-0559-2
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DOI: https://doi.org/10.1007/s00025-016-0559-2