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Erik Van Erp : Index theory on contact manifolds and noncommutative topology

In the early 1960s Atiyah and Singer derived a cohomological formula that computes the Fredholm index of an elliptic differential operator. The subsequent development of analytic K-theory of noncommutative C*-algebras greatly clarified the proof of the index formula, leading to many further generalizations. As a recent application of these techniques I will discuss the solution of the index problem for certain hypoelliptic operators on contact manifolds, first proposed by Epstein and Melrose. The final topological formula is quite easy to state, but the proof relies heavily on noncommutative techniques.

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