On Deformation Spaces, Tangent Groupoids and Generalized Filtrations of Banach and Fredholm Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912721749934080 |
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| author | Sadegh, Ahmad Reza Haj Saeedi Trout, Jody |
| author_facet | Sadegh, Ahmad Reza Haj Saeedi Trout, Jody |
| contents | We extend the deformation to the normal cone and tangent groupoid constructions from finite-dimensional manifolds to infinite-dimensional Banach and Fredholm manifolds. Next, we generalize the concept of Fredholm filtrations to get a more flexible and functorial theory. In particular, we show that if $M$ is a Banach (or Fredholm) manifold with generalized filtration ${\mathcal F} = \{M_n\}_1^\infty$ by finite-dimensional submanifolds, then there are induced generalized filtrations $T{\mathcal F} = \{TM_n\}_1^\infty$ of the tangent bundle $TM$ and $\mathbb{T}{\mathcal F} = \{\mathbb{T}{M_n}\}_1^\infty$ of the tangent groupoid $\mathbb{T}{M}$, which is not possible in the classical theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Deformation Spaces, Tangent Groupoids and Generalized Filtrations of Banach and Fredholm Manifolds Sadegh, Ahmad Reza Haj Saeedi Trout, Jody Functional Analysis Differential Geometry 58B15, 58B10, 58B05 (Primary) 46T05, 57N20, 47A53 (Secondary) We extend the deformation to the normal cone and tangent groupoid constructions from finite-dimensional manifolds to infinite-dimensional Banach and Fredholm manifolds. Next, we generalize the concept of Fredholm filtrations to get a more flexible and functorial theory. In particular, we show that if $M$ is a Banach (or Fredholm) manifold with generalized filtration ${\mathcal F} = \{M_n\}_1^\infty$ by finite-dimensional submanifolds, then there are induced generalized filtrations $T{\mathcal F} = \{TM_n\}_1^\infty$ of the tangent bundle $TM$ and $\mathbb{T}{\mathcal F} = \{\mathbb{T}{M_n}\}_1^\infty$ of the tangent groupoid $\mathbb{T}{M}$, which is not possible in the classical theory. |
| title | On Deformation Spaces, Tangent Groupoids and Generalized Filtrations of Banach and Fredholm Manifolds |
| topic | Functional Analysis Differential Geometry 58B15, 58B10, 58B05 (Primary) 46T05, 57N20, 47A53 (Secondary) |
| url | https://arxiv.org/abs/2511.04492 |