An equivariant index formula for elliptic actions on contact manifolds
| dc.creator | Fitzpatrick, Sean | |
| dc.date | 2007-12-14 | |
| dc.date | 2008-06-23 | |
| dc.date.accessioned | 2026-07-07T09:45:45Z | |
| dc.date.available | 2026-07-07T09:45:45Z | |
| dc.description | Given an elliptic action of a compact Lie group $G$ on a co-oriented contact manifold $(M,E)$ one obtains two naturally associated objects: A $G$-transversally elliptic operator $\dirac$, and an equivariant differential form with generalised coefficients $\mathcal{J}(E,X)$ defined in terms of a choice of contact form on $M$. We explain how the form $\mathcal{J}(E,X)$ is natural with respect to the contact structure, and give a formula for the equivariant index of $\dirac$ involving $\mathcal{J}(E,X)$. A key tool is the Chern character with compact support developed by Paradan-Vergne \cite{PV1,PV}. | |
| dc.description | 23 pages; Final (publication) version - to appear in MRL. Further typo fixes, extension of final corollary from formula at the identity to the entire group | |
| dc.identifier | https://arxiv.org/abs/0712.2431 | |
| dc.identifier | http://arxiv.org/abs/0712.2431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163303 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.title | An equivariant index formula for elliptic actions on contact manifolds | |
| dc.type | text |