An application of the second Riemann continuation theorem to cohomology of the Lie algebra of vector fields on the complex line
| dc.creator | Kawazumi, Nariya | |
| dc.date | 2005-08-21 | |
| dc.date.accessioned | 2026-07-07T05:22:32Z | |
| dc.date.available | 2026-07-07T05:22:32Z | |
| dc.description | We study cohomology groups of the Lie algebra of vector fields on the complex line, $W_1$, with values in the tensor fields in several variables. From a generalization by Scheja of the second Riemann (Hartogs) continuation theorem, we deduce a cohomology exact sequence of the subalgebra of $W_1$ consisting of vectors having a zero at the origin. As applications, we compute the cohomology algebra of $W_1$ with values in the functions on $\Bbb C^n$ explicitly, and establish a certain vanishing theorem for the cohomology of $W_1$ with values in the quadratic differentials in several variables, which is closely related to the moduli space of Riemann surfaces. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508390 | |
| dc.identifier | http://arxiv.org/abs/math/0508390 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76097 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Complex Variables | |
| dc.subject | 58H10; 14H15, 17B56, 17B68, 32G15, 57R32 | |
| dc.title | An application of the second Riemann continuation theorem to cohomology of the Lie algebra of vector fields on the complex line | |
| dc.type | text |