The analytic index for proper, Lie groupoid actions

Details The analytic index for proper, Lie groupoid actions The analytic index for proper, Lie groupoid actions

2007-04-20

arxiv.org/abs/0704.2799v1

Comtemp. Math. 282(2001), 115-135

Mathematics

Operator Algebras

Scientific paper

Many index theorems (both classical and in noncommutative geometry) can be interpreted in terms of a Lie groupoid acting properly on a manifold and leaving an elliptic family of pseudodifferential operators invariant. Alain Connes in his book raised the question of an index theorem in this general context. In this paper, an analytic index for many such situations is constructed. The approach is inspired by the classical families theorem of Atiyah and Singer, and the proof generalizes, to the case of proper Lie groupoid actions, some of the results proved for proper locally compact group actions by N. C. Phillips.

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