A topological method to compute spectral flow
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
This paper describes a topological method to compute the spectral flow of a family of twisted Dirac operators, it includes two detailed examples. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of Chern-Simons invariants and rho invariants. The first step is to construct a flat cobordism to a new bigger 3-manifold. The advantage of the new connection is that it is in the path component of a reducible connection. The second step is to calculate the effect of these operations on the invariants. The final step is an application of the G-signature theorem to compute the invariants.
Cite
@article{arxiv.math/9712222,
title = {A topological method to compute spectral flow},
author = {Dave Auckly},
journal= {arXiv preprint arXiv:math/9712222},
year = {2007}
}
Comments
25 pages