Invariants de Von Neumann des faisceaux coherents
| dc.creator | Eyssidieux, Philippe | |
| dc.date | 1998-06-30 | |
| dc.date.accessioned | 2026-07-07T05:25:13Z | |
| dc.date.available | 2026-07-07T05:25:13Z | |
| dc.description | Inspired by some recent work of M. Farber, W. Lück and M. Shubin on L2 homotopy invariants of infinite Galois coverings of simplicial complexes (L2 Betti numbers and Novikov-Shubin invariants), this article extends Atiyah's L2 index theory to coherent analytic sheaves on complex analytic spaces. Let $X$ be a complex analytic space with a proper cocompact biholomorphic action of a discrete group $G$. Let $F$ be a $G$-equivariant coherent analytic sheaf on $X$. We give a meaningful notion of a L2 section of $F$ on $X$. We also construct L2 cohomology groups. We prove that these L2 cohomology groups belong to an abelian category of topological $G$-modules introduced by M. Farber. On this category there are two kinds of invariants: Von Neumann dimension and Novikov-Shubin invariants. The alternating sum of the Von Neumann dimensions of the L2 cohomology groups of $F$ can be computed by an analogue of Atiyah's L2 index theorem. Novikov-Shubin invariants show up when the L2 cohomology groups are non-Hausdorff and, like in algebraic topology, are still very intriguing (and not very well understood). | |
| dc.description | Latex2e, 46 pages, French | |
| dc.identifier | https://arxiv.org/abs/math/9806159 | |
| dc.identifier | http://arxiv.org/abs/math/9806159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77100 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C30 (Primary) 32J25 (Secondary) | |
| dc.title | Invariants de Von Neumann des faisceaux coherents | |
| dc.type | text |