Appears in collection : 2025 - T1 - Representation theory and noncommutative geometry

In this talk we define the boundary index of a singular manifold in a general $C^*$-algebraic framework following the Lescure and Carrillo Rouse approach. Then we explain how it encodes geometrical obstruction for symbols to be associated to nicer operators (Fredholm operators in the classical case). Eventually we extend Lescure and Carrillo Rouse's strategies to compute the associated K-theory groups in the case of families of manifolds with corners using iterated blow-ups.