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On Kähler nilmanifolds with top homology in codimension two
Published online by Cambridge University Press: 17 April 2009
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Suppose G is a connected, complex, nilpotent Lie group and Γ is a discrete subgroup of G such that G/Γ is Kähler and the top nonvanishing homology group of G/Γ (with coefficients in ℤ2) is in codimension two or less. We show that G is then Abelian. We also note that an example from [12] shows that this fails if the top nonvanishing homology is in codimension three.
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- Copyright © Australian Mathematical Society 2006