An Explicit Proof of the Generalized Gauss-Bonnet Formula
| dc.creator | Gillet, Henri | |
| dc.creator | Unlu, Fatih | |
| dc.date | 2004-04-02 | |
| dc.date | 2009-05-28 | |
| dc.date.accessioned | 2026-07-07T13:18:41Z | |
| dc.date.available | 2026-07-07T13:18:41Z | |
| dc.description | In this paper we construct an explicit representative for the Grothendieck fundamental class [Z] of a complex submanifold Z of a complex manifold X, under the assumption that Z is the zero locus of a real analytic section of a holomorphic vector bundle E. To this data we associate a super-connection A on the exterior algebra of E, which gives a "twisted resolution" of the structure sheaf of Z. The "generalized super-trace" of A^{2r}/r!, where r is the rank of E, is an explicit map of complexes from the twisted resolution to the Dolbeault complex of X, which represents [Z]. One may then read off the Gauss-Bonnet formula from this map of complexes. | |
| dc.description | 21 pages. Paper reorganized to improve exposition. To appear in Asterisque | |
| dc.identifier | https://arxiv.org/abs/math/0404051 | |
| dc.identifier | http://arxiv.org/abs/math/0404051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231503 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32C35; 57R20 | |
| dc.title | An Explicit Proof of the Generalized Gauss-Bonnet Formula | |
| dc.type | text |