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University Park
Altoona

Thursday, October 13, 2005
5:00pm, 106 McAllister

Augustin Banyaga
Penn State University

On the class of the transverse divergence

Abstract: The class of the transverse divergence I(F) of a transversally oriented foliation F (a generalization of the Koszul divergence class) is the obstruction to the existence of a transverse volume form (defining the foliation) which is invariant by all foliated vector fields. The Reeb class R(F) of F is the obstruction to the existence of a transverse volum which is holonomy invariant. We compare these two classes and give relationships with the Godbillon-Vey invariant. For instance, for codimension one foliations admitting a dense leaf the two classes coincide. We provide several examples of foliations F with non trivial I(F). For instance, we show that if F is a Lie G-foliation with dense leaves, then I(F) is trivial iff the Lie algebra is unimodular.

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We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Fall 2005 semester: Aissa Wade and Wojciech Dorabiala.

 

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