A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connections
Abstract
We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in terms of the spectral flow on S, the spectral flow on X (with certain Atiyah-Patodi-Singer boundary conditions), and two correction terms which depend only on the endpoints. Our result improves on other splitting theorems by removing assumptions on the non-resonance level of the odd signature operator or the dimension of the kernel of the tangential operator, and allows progress towards a conjecture by Lisa Jeffrey in her work on Witten's 3-manifold invariants in the context of the asymptotic expansion conjecture.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 2004
- DOI:
- arXiv:
- arXiv:math/0412191
- Bibcode:
- 2004math.....12191H
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Differential Geometry;
- 57M27;
- 57R57;
- 53D12;
- 58J30
- E-Print:
- Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper52.abs.html