Mathematics – Geometric Topology
Scientific paper
2004-12-09
Geom. Topol. 9(2005) 2261-2302
Mathematics
Geometric Topology
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper52.abs.html
Scientific paper
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.
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