Volume 9, issue 4 (2005)

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

Volume 23
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

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
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
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
1 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797
2 D Bleecker, B Booss-Bavnbek, Spectral invariants of operators of Dirac type on partitioned manifolds, from: "Aspects of boundary problems in analysis and geometry", Oper. Theory Adv. Appl. 151, Birkhäuser (2004) 1 MR2072498
3 H U Boden, C M Herald, P A Kirk, E P Klassen, Gauge theoretic invariants of Dehn surgeries on knots, Geom. Topol. 5 (2001) 143 MR1825661
4 B Booss-Bavnbek, M Lesch, J Phillips, Unbounded Fredholm operators and spectral flow, Canad. J. Math. 57 (2005) 225 MR2124916
5 B Booß-Bavnbek, K P Wojciechowski, Elliptic boundary problems for Dirac operators, Mathematics: Theory & Applications, Birkhäuser (1993) MR1233386
6 U Bunke, On the gluing problem for the $\eta$–invariant, J. Differential Geom. 41 (1995) 397 MR1331973
7 S E Cappell, R Lee, E Y Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994) 121 MR1263126
8 S E Cappell, R Lee, E Y Miller, Self-adjoint elliptic operators and manifold decompositions. I. Low eigenmodes and stretching, Comm. Pure Appl. Math. 49 (1996) 825 MR1391757
9 A M Daniel, Maslov index, symplectic reduction in a symplectic Hilbert space and a splitting formula for spectral flow, PhD thesis, Indiana University, Bloomington (1997)
10 M Daniel, An extension of a theorem of Nicolaescu on spectral flow and the Maslov index, Proc. Amer. Math. Soc. 128 (2000) 611 MR1622789
11 M Daniel, P Kirk, A general splitting formula for the spectral flow, Michigan Math. J. 46 (1999) 589 MR1721567
12 J F Davis, P Kirk, Lecture notes in algebraic topology, Graduate Studies in Mathematics 35, American Mathematical Society (2001) MR1841974
13 S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1990) MR1079726
14 B Fine, P Kirk, E Klassen, A local analytic splitting of the holonomy map on flat connections, Math. Ann. 299 (1994) 171 MR1273082
15 B Himpel, A splitting formula for spectral flow on closed 3–manifolds, PhD thesis, Indiana University, Bloomington (2004)
16 B Himpel, P Kirk, M Lesch, Calderón projector for the Hessian of the perturbed Chern–Simons function on a 3–manifold with boundary, Proc. London Math. Soc. $(3)$ 89 (2004) 241 MR2063666
17 L C Jeffrey, Chern–Simons–Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Comm. Math. Phys. 147 (1992) 563 MR1175494
18 T Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer (1995) MR1335452
19 P A Kirk, E P Klassen, Chern–Simons invariants of 3–manifolds and representation spaces of knot groups, Math. Ann. 287 (1990) 343 MR1054574
20 P Kirk, E Klassen, Computing spectral flow via cup products, J. Differential Geom. 40 (1994) 505 MR1305980
21 P Kirk, E Klassen, Continuity and analyticity of families of self-adjoint Dirac operators on a manifold with boundary, Illinois J. Math. 42 (1998) 123 MR1492043
22 P Kirk, E Klassen, D Ruberman, Splitting the spectral flow and the Alexander matrix, Comment. Math. Helv. 69 (1994) 375 MR1289334
23 P Kirk, M Lesch, The $\eta$–invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary, Forum Math. 16 (2004) 553 MR2044028
24 L I Nicolaescu, The Maslov index, the spectral flow, and decompositions of manifolds, Duke Math. J. 80 (1995) 485 MR1369400
25 T Ohtsuki, Problems on invariants of knots and 3–manifolds, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4, Geom. Topol. Publ., Coventry (2002) 377 MR2065029
26 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772
27 K P Wojciechowski, The additivity of the $\eta$–invariant: the case of an invertible tangential operator, Houston J. Math. 20 (1994) 603 MR1305932