Volume 9, issue 4 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A splitting formula for the spectral flow of the odd signature operator on 3–manifolds coupled to a path of $SU(2)$ connections

Benjamin Himpel

Geometry & Topology 9 (2005) 2261–2302

arXiv: math.GT/0412191


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 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.

spectral flow, odd signature operator, gauge theory, Chern–Simons theory, Atiyah–Patodi–Singer boundary conditions, Maslov index
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R57, 53D12, 58J30
Forward citations
Received: 4 December 2004
Accepted: 1 November 2005
Published: 6 December 2005
Proposed: Ronald Stern
Seconded: Peter Teichner, Ronald Fintushel
Benjamin Himpel
Mathematisches Institut
Universität Bonn
Beringstr. 6
D–53115 Bonn