Residue Formulation of Chern Character on Smooth Manifolds
| dc.creator | Gerenrot, Dmitry | |
| dc.date | 2005-05-07 | |
| dc.date.accessioned | 2026-07-07T05:19:41Z | |
| dc.date.available | 2026-07-07T05:19:41Z | |
| dc.description | The Chern character of a complex vector bundle is most conveniently defined as the exponential of a curvature of a connection. It is well known that its cohomology class does not depend on the particular connection chosen. It has been shown by Quillen that a connection may be perturbed by an endomorphism of the vector bundle, such as a symbol of some elliptic differential operator. This point of view, as we intend to show, allows one to relate Chern character to a non-commutative sibling formulated by Connes and Moscovici. The general setup for our problem is purely geometric. Let σbe the symbol of a Dirac-type operator acting on sections of a \Z_2-graded vector bundle E. Let \nabla be a connection on E, pulled back to T^*M. Suppose also that \nabla respects the Z_2-grading. The object \nabla+σis a superconnection on T^*M in the sense of Quillen. We obtain a formula for the H_*(M)-valued Poincare dual of Quillen's Chern character ch(D)=trace(exp(\nabla+σ)^2) in terms of residues of Γ(z)trace(\nabla+σ)^{-2z}. We also compute two examples. | |
| dc.description | 38 pages with 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0505121 | |
| dc.identifier | http://arxiv.org/abs/math/0505121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75108 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57R20(primary) 57R22, 58J20 (secondary) | |
| dc.title | Residue Formulation of Chern Character on Smooth Manifolds | |
| dc.type | text |