Volume 3, issue 2 (2003)

Download this article
For printing
Recent Issues

Volume 21
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
On the rho invariant for manifolds with boundary

Paul A Kirk and Matthias Lesch

Algebraic & Geometric Topology 3 (2003) 623–675
Bibliography
1 M F Atiyah, The geometry and physics of knots, from: "Miniconference on Geometry and Physics (Canberra, 1989)", Proc. Centre Math. Anal. Austral. Nat. Univ. 22, Austral. Nat. Univ. (1989) 1 MR1027859
2 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43 MR0397797
3 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405 MR0397798
4 M F Atiyah, V K Patodi, I M Singer, Spectral asymmetry and Riemannian geometry III, Math. Proc. Cambridge Philos. Soc. 79 (1976) 71 MR0397799
5 N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, Grundlehren der Mathematischen Wissenschaften 298, Springer (1992) MR1215720
6 J M Bismut, D S Freed, The analysis of elliptic families I: Metrics and connections on determinant bundles, Comm. Math. Phys. 106 (1986) 159 MR853982
7 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
8 B Booss-Bavnbek, M Lesch, J Phillips, Unbounded Fredholm operators and spectral flow, Canad. J. Math. 57 (2005) 225 MR2124916
9 B Booß-Bavnbek, K P Wojciechowski, Elliptic boundary problems for Dirac operators, Mathematics: Theory & Applications, Birkhäuser (1993) MR1233386
10 U Bunke, On the gluing problem for the $\eta$–invariant, J. Differential Geom. 41 (1995) 397 MR1331973
11 S E Cappell, R Lee, E Y Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994) 121 MR1263126
12 S E Cappell, A splitting theorem for manifolds, Invent. Math. 33 (1976) 69 MR0438359
13 X Dai, D S Freed, $\eta$–invariants and determinant lines, J. Math. Phys. 35 (1994) 5155 MR1295462
14 M S Farber, J P Levine, Jumps of the eta-invariant, Math. Z. 223 (1996) 197 MR1417429
15 B Fine, P Kirk, E Klassen, A local analytic splitting of the holonomy map on flat connections, Math. Ann. 299 (1994) 171 MR1273082
16 P B Gilkey, Invariance theory, the heat equation, and the Atiyah–Singer index theorem, Studies in Advanced Mathematics, CRC Press (1995) MR1396308
17 J Hempel, 3–Manifolds, Ann. of Math. Studies 86, Princeton University Press (1976) MR0415619
18 T Kato, Perturbation theory for linear operators, Grundlehren der Mathematischen Wissenschaften 132, Springer (1976) MR0407617
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 A Kirk, E P Klassen, Representation spaces of Seifert fibered homology spheres, Topology 30 (1991) 77 MR1081935
21 P Kirk, E Klassen, D Ruberman, Splitting the spectral flow and the Alexander matrix, Comment. Math. Helv. 69 (1994) 375 MR1289334
22 P Kirk, E Klassen, Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary, Mem. Amer. Math. Soc. 124 (1996) MR1355034
23 P A Kirk, E P Klassen, The spectral flow of the odd signature operator and higher Massey products, Math. Proc. Cambridge Philos. Soc. 121 (1997) 297 MR1426525
24 P Kirk, E Klassen, The first-order spectral flow of the odd signature operator on a manifold with boundary, Topology Appl. 116 (2001) 199 MR1855963
25 P Kirk, E Klassen, Computing spectral flow via cup products, J. Differential Geom. 40 (1994) 505 MR1305980
26 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
27 E P Klassen, Representations of knot groups in $\mathrm{SU}(2)$, Trans. Amer. Math. Soc. 326 (1991) 795 MR1008696
28 H B Lawson Jr., M L Michelsohn, Spin geometry, Princeton Mathematical Series 38, Princeton University Press (1989) MR1031992
29 M Lesch, K P Wojciechowski, On the $\eta$–invariant of generalized Atiyah–Patodi–Singer boundary value problems, Illinois J. Math. 40 (1996) 30 MR1386311
30 C Livingston, Knot theory, Carus Mathematical Monographs 24, Mathematical Association of America (1993) MR1253070
31 W D Neumann, Homotopy invariance of Atiyah invariants, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 181 MR520534
32 D Kvillen, Determinants of Cauchy–Riemann operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 19 (1985) 37, 96 MR783704
33 T R Ramadas, I M Singer, J Weitsman, Some comments on Chern–Simons gauge theory, Comm. Math. Phys. 126 (1989) 409 MR1027504
34 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
35 F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. $(2)$ 87 (1968) 56 MR0224099
36 C T C Wall, Non-additivity of the signature, Invent. Math. 7 (1969) 269 MR0246311
37 C T C Wall, Surgery on compact manifolds, Mathematical Surveys and Monographs 69, American Mathematical Society (1999) MR1687388
38 S Weinberger, Homotopy invariance of $\eta$–invariants, Proc. Nat. Acad. Sci. U.S.A. 85 (1988) 5362 MR952817