The analytic index of elliptic pseudodifferential operators on a singular foliation

Details The analytic index of elliptic pseudodifferential operators on a singular foliation The analytic index of elliptic pseudodifferential operators on a singular foliation

2010-04-21

arxiv.org/abs/1004.3797v3

Mathematics

Operator Algebras

19 pages. Correction of typos in v2, v3.

Scientific paper

In previous papers (arxiv:math/0612370 and arxiv:0909.1342) we defined the
C*-algebra and the longitudinal pseudodifferential calculus of any singular
foliation (M,F). Here we construct the analytic index of an elliptic operator
as a KK-theory element, and prove that the same element can be obtained from an
"adiabatic foliation" TF on $M \times \R$, which we introduce here.

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