A transverse index theorem in the calculus of filtered manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909534842257408 |
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| author | Cren, Clément |
| author_facet | Cren, Clément |
| contents | We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of transversally Rockland and prove that transversally Rockland operators yield a K-homology class. We construct an equivariant KK-class for transversally Rockland transverse symbols and show a Poincare duality type result linking the class of an operator and its symbol. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_09112 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A transverse index theorem in the calculus of filtered manifolds Cren, Clément Differential Geometry K-Theory and Homology Operator Algebras 58J40, 53C12 (Primary) 58H05, 46L80, 19K56 (Secondary) We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of transversally Rockland and prove that transversally Rockland operators yield a K-homology class. We construct an equivariant KK-class for transversally Rockland transverse symbols and show a Poincare duality type result linking the class of an operator and its symbol. |
| title | A transverse index theorem in the calculus of filtered manifolds |
| topic | Differential Geometry K-Theory and Homology Operator Algebras 58J40, 53C12 (Primary) 58H05, 46L80, 19K56 (Secondary) |
| url | https://arxiv.org/abs/2207.09112 |