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Journal of the London Mathematical Society Advance Access originally published online on January 13, 2009
Journal of the London Mathematical Society 2009 79(2):346-362; doi:10.1112/jlms/jdn076
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© 2009 London Mathematical Society

Lie-algebra Dolbeault-cohomology and small deformations of nilmanifolds

Sönke Rollenske

Department of Mathematics
Imperial College London
London
SW7 2AZ
United Kingdom

We consider nilmanifolds with left-invariant complex structure and prove that small deformations of such structures are again left invariant if the Dolbeault-cohomology of the nilmanifold can be calculated using left-invariant forms. By a result of Console and Fino this is generically the case. Our main tool is an analogue of Dolbeault-cohomology for Lie-algebras with complex structure.

2000 Mathematics Subject Classification 32G05, 32G08, 17B30, 53C30.

Received April 17, 2008; published online January 13, 2009.


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