关于变形空间、切群体和Banach及Fredholm流形的广义滤波
On Deformation Spaces, Tangent Groupoids and Generalized Filtrations of Banach and Fredholm Manifolds
AI总结：
本文研究了Banach和Fredholm流形的广义滤波，并扩展了切群体和切丛的构造方法，提出了更灵活的理论框架。
摘要：
我们扩展了从有限维流形到无限维Banach和Fredholm流形的变形到正常锥和切群体构造。接着，我们将Fredholm滤波的概念推广，以获得更灵活和函子化的理论。特别是，我们证明如果M是一个Banach（或Fredholm）流形，具有由有限维子流形构成的广义滤波F={M_n}₁^∞，则切丛TM会诱导出广义滤波T F={TM_n}₁^∞，而切群体T M会诱导出广义滤波T F={T M_n}₁^∞，这在经典理论中是不可能的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
