Li, Tian-Jun; Zhang, Weiyi Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds. (English) Zbl 1225.53066 Commun. Anal. Geom. 17, No. 4, 651-683 (2009). Summary: We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate \(J\)-tamed symplectic cones and \(J\)-compatible symplectic cones over a large class of almost complex manifolds, including all Kähler manifolds, almost Kähler 4-manifolds and complex surfaces. Cited in 7 ReviewsCited in 57 Documents MSC: 53C56 Other complex differential geometry 32Q60 Almost complex manifolds 53C55 Global differential geometry of Hermitian and Kählerian manifolds 55N99 Homology and cohomology theories in algebraic topology Keywords:tamed symplectic forms; \(J\)-tamed symplectic cones; almost Kähler 4-manifolds; complex surfaces PDFBibTeX XMLCite \textit{T.-J. Li} and \textit{W. Zhang}, Commun. Anal. Geom. 17, No. 4, 651--683 (2009; Zbl 1225.53066) Full Text: DOI arXiv