Geometric obstructions to fully ellipticity for families of manifolds with corners
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908791427039232 |
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| author | Thiry, Florian |
| author_facet | Thiry, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric obstructions to fully ellipticity for families of manifolds with corners Thiry, Florian K-Theory and Homology Operator Algebras 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. |
| title | Geometric obstructions to fully ellipticity for families of manifolds with corners |
| topic | K-Theory and Homology Operator Algebras |
| url | https://arxiv.org/abs/2601.19576 |