A note on traces for the Heisenberg calculus
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916693394063360 |
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| author | Gorokhovsky, Alexander van Erp, Erik |
| author_facet | Gorokhovsky, Alexander van Erp, Erik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on traces for the Heisenberg calculus Gorokhovsky, Alexander van Erp, Erik Functional Analysis Analysis of PDEs Differential Geometry 46L80 (Primary) 58J20, 58J40 (Secondary) 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. |
| title | A note on traces for the Heisenberg calculus |
| topic | Functional Analysis Analysis of PDEs Differential Geometry 46L80 (Primary) 58J20, 58J40 (Secondary) |
| url | https://arxiv.org/abs/2410.11982 |