Levi-flat CR structures on compact Lie groups
Howard Jacobowitz, Max Reinhold Jahnke
TL;DR
This paper extends Pittie's result on Dolbeault cohomology to Levi-flat CR structures of maximal rank on compact Lie groups, using algebraic classification methods.
Contribution
It generalizes the computation of Dolbeault cohomology to Levi-flat CR structures, broadening the understanding of complex structures on compact Lie groups.
Findings
Dolbeault cohomology can be computed for Levi-flat CR structures on compact Lie groups.
The algebraic classification aids in understanding the structure of these CR structures.
Abstract
Pittie [Pit88] proved that the Dolbeault cohomology of all left-invariant complex structures on compact Lie groups can be computed by looking at the Dolbeault cohomology induced on a conveniently chosen maximal torus. We use the algebraic classification of left-invariant CR structures of maximal rank on compact Lie groups [CK04] to generalize Pittie's result to left-invariant Levi-flat CR structures of maximal rank on compact Lie groups.
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Taxonomy
TopicsGeometry and complex manifolds · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology