Families Index for Pseudodifferential Operators on Manifolds with Boundary
| dc.creator | Melrose, Richard | |
| dc.creator | Rochon, Frederic | |
| dc.date | 2003-04-20 | |
| dc.date | 2003-11-20 | |
| dc.date.accessioned | 2026-07-07T04:57:05Z | |
| dc.date.available | 2026-07-07T04:57:05Z | |
| dc.description | An analytic index is defined for a family of cusp pseudodifferential operators, $P_b,$ on a fibration with fibres which are compact manifolds with boundaries, provided the family is elliptic and has invertible indicial family at the boundary. In fact there is always a perturbation $Q_b$ by a family of cusp operators of order $-\infty$ such that each $P_b+Q_b$ is invertible. Thus any elliptic family of symbols has a realization as an invertible family of cusp pseudodifferential operators, which is a form of the cobordism invariance of the index. A crucial role is played by the weak contractibility of the group of cusp smoothing operators on a compact manifold with non-trivial boundary and the associated exact sequence of classifying spaces of odd and even K-theory. | |
| dc.description | 21 pages; corrected typos, changed the abstract, added a paragraph in the introduction | |
| dc.identifier | https://arxiv.org/abs/math/0304280 | |
| dc.identifier | http://arxiv.org/abs/math/0304280 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67149 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J20; 58J40 | |
| dc.title | Families Index for Pseudodifferential Operators on Manifolds with Boundary | |
| dc.type | text |