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

2025/11/06 by Sadegh, Ahmad Reza Haj Saeedi, Trout, Jody
#47A53 (Secondary) #57N20 #58B05 (Primary) 46T05 #58B10 #58B15 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2511.04492

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^∞ by finite-dimensional submanifolds, then there are induced generalized filtrations T\mathcal F = \TM_n\₁^∞ of the tangent bundle TM and \mathbbT\mathcal F = \\mathbbTM_n\₁^∞ of the tangent groupoid \mathbbTM, which is not possible in the classical theory.

Citations

• Blowup constructions for Lie groupoids and a Boutet de Monvel type calculus
• Euler-like vector fields, deformation spaces and manifolds with filtered structure
• On C*-algebras and K-theory for infinite-dimensional Fredholm Manifolds

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