Collapsing and Dirac-Type Operators
| dc.creator | Lott, John | |
| dc.date | 2000-05-01 | |
| dc.date | 2000-09-10 | |
| dc.date.accessioned | 2026-07-07T04:34:56Z | |
| dc.date.available | 2026-07-07T04:34:56Z | |
| dc.description | We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the spectrum of a certain first-order differential operator on B, which can be constructed using superconnections. In the case of a general limit space X, we express the limit operator in terms of a transversally elliptic operator on a G-space Y, with X = Y/G. As an application, we give a characterization of manifolds which do not admit uniform upper bounds, in terms of diameter and sectional curvature, on the k-th eigenvalue of the square of a Dirac-type operator. We also give a formula for the essential spectrum of a Dirac-type operator on a finite-volume manifold with pinched negative sectional curvature. | |
| dc.description | 19 pages, Theorem 5 improved, some details of proof given | |
| dc.identifier | https://arxiv.org/abs/math/0005009 | |
| dc.identifier | http://arxiv.org/abs/math/0005009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59100 | |
| dc.subject | Differential Geometry | |
| dc.title | Collapsing and Dirac-Type Operators | |
| dc.type | text |