On Deformation Spaces, Tangent Groupoids and Generalized Filtrations of Banach and Fredholm Manifolds

Abstract

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 $T\mathcal{F}=\{T{M}_n{\}}_1^{\infty }$ 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.

17 pages, accepted for publication in the journal Topology and Its Applications