Von Neumann spectra near the spectral gap
| dc.creator | Carey, Alan L. | |
| dc.creator | Coulhon, Thierry | |
| dc.creator | Mathai, Varghese | |
| dc.creator | Phillips, John | |
| dc.date | 1996-10-29 | |
| dc.date.accessioned | 2026-07-07T09:12:53Z | |
| dc.date.available | 2026-07-07T09:12:53Z | |
| dc.description | In this paper we study some new von Neumann spectral invariants associated to the Laplacian acting on L^2 differential forms on the universal cover of a closed manifold. These invariants coincide with the Novikov-Shubin invariants whenever there is no spectral gap in the spectrum of the Laplacian, and are homotopy invariants in this case. In the presence of a spectral gap, they differ in character and value from the Novikov-Shubin invariants. Under a positivity assumption on these invariants, we prove that certain L^2 theta and L^2 zeta functions defined by metric dependent combinatorial Laplacians acting on $L^2$ cochains associated with a triangulation of the manifold, converge uniformly to their analytic counterparts, as the mesh of the triangulation goes to zero. | |
| dc.description | LaTeX, 31 pages, to appear in Bull. de la Soc. Math. de France | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9610019 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9610019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152177 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58 (Primary) | |
| dc.title | Von Neumann spectra near the spectral gap | |
| dc.type | text |