An analytic index for Lie groupoids

Details An analytic index for Lie groupoids An analytic index for Lie groupoids

2006-12-15

arxiv.org/abs/math/0612455v1

Mathematics

K-Theory and Homology

13 pages. To be submitted for the Proceedings of the International conference on K-theory and Non commutative geometry held in

Scientific paper

For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is very difficult. In this work, we define another analytic index morphism associated to a Lie groupoid; this one takes values in a group that allows us to do pairings with cyclic cocycles. This last group is related to the compactly supported functions on the groupoid. We use the tangent groupoid to define our index as a sort of ''deformation''.

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