Riemann-Roch for real varieties
| dc.creator | Bressler, P. | |
| dc.creator | Kapranov, M. | |
| dc.creator | Tsygan, B. | |
| dc.creator | Vasserot, E. | |
| dc.date | 2006-12-14 | |
| dc.date | 2006-12-24 | |
| dc.date.accessioned | 2026-07-07T07:37:01Z | |
| dc.date.available | 2026-07-07T07:37:01Z | |
| dc.description | If E is a C^\infty complex vector bundle on an oriented C^\infty manifold Σ, diffeomorphic to a circle, then the space of sections of E has a canonical polarization in the sense of Pressley and Segal and so one has its determinantal gerbe with lien C^*, the group of nonzero complex numbers. If q:Σ-->B is a smooth family of circles as above and E is a vector bundle on Σ, then the smooth direct image q_*(E) is an infinite-dimensional bundle with fibers as above and so we have its determinantal gerbe on B with lien being the sheaf of invertible complex valued C^\infty functions, it gives a class in H^3(B, Z). In this paper we consider a family q:Σ-->B as above but with fibers being compact oriented C^\infty manifolds of dimension d. For a bundle E on Σone expects q_*(E) to possess a determinantal d-gerbe and hence to give a class in H^{d+2}(B, Z). We construct directly, by means of a version of the Chern-Weil theory, the real version of this would be class. We further prove a real version of the Grothendieck-Riemann-Roch theorem describing this class as a direct image of a certain characteristic class of E. | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612410 | |
| dc.identifier | http://arxiv.org/abs/math/0612410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120633 | |
| dc.subject | Differential Geometry | |
| dc.title | Riemann-Roch for real varieties | |
| dc.type | text |