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arXiv · 2410.11982

A note on traces for the Heisenberg calculus

Alexander Gorokhovsky·Erik van Erp
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Abstract

In previous work, we gave a local formula for the index of Heisenberg elliptic operators on contact manifolds. We constructed a cocycle in periodic cyclic cohomology which, when paired with the Connes-Chern character of the principal Heisenberg symbol, calculates the index. A crucial ingredient of our index formula was a new trace on the algebra of Heisenberg pseudodifferential operators. The construction of this trace was rather involved. In the present paper, we clarify the nature of this trace.

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Alexander Gorokhovsky, Erik van Erp. 2024-10-15. A note on traces for the Heisenberg calculus. https://arxiv.org/abs/2410.11982

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