Vanishing theorems on covering manifolds
| dc.creator | Braverman, Maxim | |
| dc.date | 1998-09-24 | |
| dc.date.accessioned | 2026-07-07T05:26:09Z | |
| dc.date.available | 2026-07-07T05:26:09Z | |
| dc.description | Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $Γ$ of orientation-preserving isometries acts freely, so that the quotient $X=M/Γ$ is compact. We prove a vanishing theorem for a half-kernel of a $Γ$-invariant Dirac operator on a $Γ$-equivariant Clifford module over $M$, twisted by a sufficiently large power of a $Γ$-equivariant line bundle, whose curvature is non-degenerate at any point of $M$. This generalizes our previous vanishing theorems for Dirac operators on a compact manifold. In particular, if $M$ is an almost complex manifold we prove a vanishing theorem for the half-kernel of a $\spin^c$ Dirac operator, twisted by a line bundle with curvature of a mixed sign. In this case we also relax the assumption of non-degeneracy of the curvature. When $M$ is a complex manifold our results imply analogues of Kodaira and Andreotti-Grauert vanishing theorems for covering manifolds. As another application, we show that semiclassically the $\spin^c$ quantization of an almost complex covering manifold gives an "honest" Hilbert space. This generalizes a result of Borthwick and Uribe, who considered quantization of compact manifolds. Application of our results to homogeneous manifolds of a real semisimple Lie group leads to new proofs of Griffiths-Schmidt and Atiyah-Schmidt vanishing theorems. | |
| dc.description | LaTeX 2e; 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/9809144 | |
| dc.identifier | http://arxiv.org/abs/math/9809144 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77442 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Vanishing theorems on covering manifolds | |
| dc.type | text |