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On Kähler nilmanifolds with top homology in codimension two

Published online by Cambridge University Press:  17 April 2009

Bruce Gilligan
Bruce Gilligan
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, Canada, S4S 0A2, e-mail: gilligan@math.uregina.ca
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 85 - 90
Copyright
Copyright © Australian Mathematical Society 2006

References

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