An index theorem for families invariant with respect to a bundle of Lie groups
| dc.creator | Nistor, Victor | |
| dc.date | 1999-06-28 | |
| dc.date | 2000-08-16 | |
| dc.date.accessioned | 2026-07-07T05:29:41Z | |
| dc.date.available | 2026-07-07T05:29:41Z | |
| dc.description | We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle $\GR$ of Lie groups. If the fibers of $\GR \to B$ are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferential operators and obtain a local index formula for such families of invariant operators, using the Fedosov product. For topologically non-trivial bundles we have to use methods of non-commutative geometry. We discuss then as an application the construction of ``higher-eta invariants,'' which are morphisms $K_n(\PsS {\infty}Y) \to \CC$. The algebras of invariant pseudodifferential operators that we study, $\Psm {\infty}Y$ and $\PsS {\infty}Y$, are generalizations of ``parameter dependent'' algebras of pseudodifferential operators (with parameter in $\RR^q$), so our results provide also an index theorem for elliptic, parameter dependent pseudodifferential operators. | |
| dc.description | AMS-Latex, 39 pages, references, corrections, and new results added | |
| dc.identifier | https://arxiv.org/abs/math/9906188 | |
| dc.identifier | http://arxiv.org/abs/math/9906188 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78733 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | An index theorem for families invariant with respect to a bundle of Lie groups | |
| dc.type | text |