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Description: |
A. Connes showed that the space of leaves of a regular foliation can be replaced by the
$C^*$-algebra of its associated holonomy groupoid. However, for a singular foliation the
holonomy groupoid is quite an ill-behaved object. Recently we constructed the
$C^*$-algebra of \textit{any} singular foliation by considering submersions to this
groupoid instead. In this talk we discuss the construction and show that it also allows
to define pseudodifferential operators along the leaves of any singular foliation, as
well as the analytic index of elliptic such operators. This is joint work with G.
Skandalis.
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