### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 058, 10 pages      arXiv:1502.06253      https://doi.org/10.3842/SIGMA.2015.058
Contribution to the Special Issue on Poisson Geometry in Mathematics and Physics

### Modular Classes of Lie Groupoid Representations up to Homotopy

Rajan Amit Mehta
Department of Mathematics & Statistics, Smith College, 44 College Lane, Northampton, MA 01063, USA

Received February 24, 2015, in final form July 23, 2015; Published online July 25, 2015

Abstract
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''.

Key words: Lie groupoid; representation up to homotopy; modular class.

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