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arXiv · 2601.19576

Geometric obstructions to fully ellipticity for families of manifolds with corners

Florian Thiry
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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.

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Florian Thiry. 2026-01-27. Geometric obstructions to fully ellipticity for families of manifolds with corners. https://arxiv.org/abs/2601.19576

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