Geometric obstructions to fully ellipticity for families of manifolds with corners

2026/01/27 by Florian Thiry · 1 voice
Mathematics · #math.KT #math.OA

paper · pdf

Abstract

In the present paper we study index theory for families of manifold with corners. In particular the K-theoretical obstruction for an elliptic operator to have a family (Fredholm) index. For codimension 1 corners (families with boundary) it gives an expected condition on indices associated to codimension 1 faces. The main theorem of this paper concern the codimension 2 case: in addition to the expected condition on indices associated to codimension 2 faces, there is an extra combinatoric condition implying the topology of the family base. This new condition is expressed in terms of conormal homology cycles with K-theoretical coefficients.

Citations

• Fredholm anomalies on manifold with corners of low codimensions and conormal corner cycles
• Conormal homology of manifolds with corners
• Blow-ups of Lie groupoids and Lie algebroids
• Lie groupoids, pseudodifferential calculus and index theory
• Equivariant control data and neighborhood deformation retractions
• Geometric obstructions for Fredholm boundary conditions for manifolds with corners
• A cohomological formula for the Atiyah-Patodi-Singer index on manifolds with boundary
• An index theorem for manifolds with boundary
• Atiyah–Bott index on stratified manifolds
• Elliptic Theory on Manifolds with Corners: II. Homotopy classification and K-Homology
• A topological index theorem for manifolds with corners

Discussions

• Florian Thiry: Geometric obstructions to fully ellipticity for families of manifolds with corners https://arxiv.org/abs/2601.19576 https://arxiv.org/pdf/2601.19576 https://arxiv.org/html/2601.19576 [bsky, 0 points, 0 comments]

Related

• Fredholm anomalies on manifold with corners of low codimensions and conormal corner cycles
• Elliptic Theory on Manifolds with Corners: I. Dual Manifolds and Pseudodifferential Operators
• K-homology and Fredholm Operators II: Elliptic Operators
• Families of elliptic boundary problems and index theory of the Atiyah-Bott classes
• Longitudinal b-operators, Blups and Index theorems