The Heisenberg calculus, index theory, and cyclic cohomology

Abstract: On a compact contact manifold, a pseudodifferential operator with an invertible symbol in the Heisenberg calculus is a hypoelliptic Fredholm operator. Its symbol determines an element in the K-theory of the noncommutative algebra of Heisenberg symbols. In joint work with Alexander Gorokhovksy, we construct a cyclic cocycle which, when paired with the Connes-Chern character of the principal Heisenberg symbol, calculates the index.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

Noncommutative Geometry in NYC

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