Abstract:For a finitely presented discrete group Γ, we introduce two generalizations of the orbifold Euler characteristic and Γ-orbifold Euler characteristic to a class of proper topological groupoids large enough to include all cocompact proper Lie groupoids. The Γ-Euler characteristic is defined as an integral with respect to the Euler characteristic over the orbit space of the groupoid, and the Γ-inertia Euler characteristic is the usual Euler characteristic of the Γ-inertia space associated to the groupoid. A key i… Show more
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