The Schouten-Nijenhuis bracket in infinite dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916699487338496 |
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| author | Michor, Peter W. |
| author_facet | Michor, Peter W. |
| contents | The Schouten-Nijenhuis bracket on smooth infinite-dimensional manifolds $M$ is developed in two steps: For summable multivector fields whose pointwise dual are all differential form, and in an extended form for multivector fields which are sections of $L^{\bullet}_{\text{skew}}(T^*M,\mathbb R)$. We need to either assume that $C^{\infty}(M)$ separates points on $TM$, or consider sheaves of local sections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Schouten-Nijenhuis bracket in infinite dimensions Michor, Peter W. Differential Geometry Functional Analysis 58B20, 37K07 The Schouten-Nijenhuis bracket on smooth infinite-dimensional manifolds $M$ is developed in two steps: For summable multivector fields whose pointwise dual are all differential form, and in an extended form for multivector fields which are sections of $L^{\bullet}_{\text{skew}}(T^*M,\mathbb R)$. We need to either assume that $C^{\infty}(M)$ separates points on $TM$, or consider sheaves of local sections. |
| title | The Schouten-Nijenhuis bracket in infinite dimensions |
| topic | Differential Geometry Functional Analysis 58B20, 37K07 |
| url | https://arxiv.org/abs/2504.15010 |