A note on traces for the Heisenberg calculus
Functional Analysis
2025-04-18 v2 Analysis of PDEs
Differential Geometry
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.
Keywords
Cite
@article{arxiv.2410.11982,
title = {A note on traces for the Heisenberg calculus},
author = {Alexander Gorokhovsky and Erik van Erp},
journal= {arXiv preprint arXiv:2410.11982},
year = {2025}
}