Communications in Analysis and Geometry

Volume 17 (2009)

Number 4

Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds

Pages: 651 – 683

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n4.a4

Authors

Tian-Jun Li (School of Mathematics, University of Minnesota)

Weiyi Zhang (School of Mathematics, University of Minnesota)

Abstract

We introduce certain homology and cohomology subgroups for anyalmost complex structure and study their pureness, fullness andduality properties. Motivated by a question of Donaldson, we usethese groups to relate $J$-tamed symplectic cones and$J$-compatible symplectic cones over a large class of almostcomplex manifolds, including all Kähler manifolds, almostKähler $4$-manifolds and complex surfaces.

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