Modular Classes of Lie Groupoid Representations up to Homotopy?

Rajan Amit Mehta, Smith College

Archived as published.


We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein’s “The volume of a differentiable stack”.