On the n-invariant of certain nonlocal boundary value problems

Duke Mathematical Journal

Volumn 96, Issue 2, 1999, Pages 425-468

  Brüning, Jochen ^a   Lesch, Matthias ^a  

^a Institut für Mathematik   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000451551     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-09613-8     Document Type: Article

References (34)

1. M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry, I, II, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43-69;
2. J. Brüning and M. Lesch, On the spectral geometry of algebraic curves, J. Reine Angew. Math. 474 (1996), 25-66.
3. J. Brüning and R. Seeley, The resolvent expansion for second order regular singular operators, J. Funct. Anal. 73 (1987), 369-429.
4. J. Brüning and R. Seeley, An index theorem for first order regular singular operators, Amer. J. Math. 110 (1988), 659-714.
5. U. Bunke, On the gluing problem for the rj-invariant, J. Differential Geom. 41 (1995), 397-448.
6. A.-P. Calderón, “Boundary value problems for elliptic equations” in Outlines Joint Symposium on Partial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, 303-304.
7. J. Cheeger, Analytic torsion and the heat equation, Ann. of Math. (2) 109 (1979), 259-322.
8. X. Dai and D. S. Freed, ri-invariants and determinant lines: Topology and physics, J. Math. Phys. 35 (1994), 5155-5194.
9. R. G. Douglas and K. P. Wojciechowski, Adiabatic limits of the rj-invariants: The odd dimensional Atiyah-Patodi-Singer problem, Comm. Math. Phys. 142 (1991), 139-168.
10. J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), 39-79.
11. P. B. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, 2d ed., Stud. Adv. Math., CRC Press, Boca Raton, Fla., 1995.
12. P. B. Gilkey and L. Smith, The eta invariant for a class of elliptic boundary value problems, Comm. Pure Appl. Math. 36 (1983), 85-132.
13. G. Grubb and R. Seeley, Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems, Invent. Math. 121 (1995), 481-529.
14. G. Grubb and R. Seeley, Zeta and eta functions for Atiyah-Patodi-Singer operators, J. Geometric Anal. 6 (1996), 31-77.
15. A. Hassell, R. R. Mazzeo, and R. B. Melrose, Analytic surgery and the accumulation of eigenvalues, Comm. Anal. Geom. 3 (1995), 115-222.
16. C. Kassel, “Le résidu non commutatif (d’après M. Wodzicki)” in Séminaire Bourbaki, 1988-89, exp. no. 708, Astérisque 177-178 (1989), 199-229.
17. T. Kato, Perturbation theory for linear operators, Grundlehren Math. Wiss. 132, Springer-Verlag, New York, 1966.
18. M. Lesch, Deficiency indices for symmetric Dirac operators on manifolds with conic singularities, Topology 32 (1993), 611-623.
19. M. Lesch, “A singular elliptic estimate and applications” in Pseudo-Differential Calculus and Mathematical Physics, ed. M. Demuth, E. Schrohe, and B. W. Schulze, Math. Top. 5, Akademie Verlag, Berlin, 1994, 259-276.
20. M. Lesch, Operators of Fuchs type, conical singularities, and asymptotic methods, Teubner-exte Math. 136, Teubner, Stuttgart, 1997.
21. M. Lesch and K. P. Wojciechowski, On the rj-invariant of generalized Atiyah-Patodi-Singer boundary value problems, Illinois J. Math. 40 (1996), 30-46.
22. R. R. Mazzeo and R. B. Melrose, Analytic surgery and the eta invariant, Geom. Funct. Anal. 5 (1995), 14-75.
23. W. Müller, Analytic torsion and R-torsion of Riemannian manifolds, Adv. Math. 28 (1978), 233-305.
24. W. Müller, Eta invariants and manifolds with boundary, J. Differential Geom. 40 (1994), 311-377.
25. 2-index of Dirac operators on manifolds with corners of codimension two, I, J. Differential Geom. 44 (1996), 97-177.
26. R. S. Palais, Seminar on the Atiyah-Singer Index Theorem, Ann. of Math. Stud., Princeton Univ. Press, Princeton, N.J. 1965.
27. I. M. Singer, “The ^-invariant and the index” in Mathematical Aspects of String Theory (San Diego, Calif, 1986), ed. S. T. Yau, Adv. Ser. Math. Phys. 1, World Sci., Singapore, 1987, 239-258.
28. A. Sommerfeld, Vorlesungen iiber Theoretische Physik, Band VI: Partielle Differential-gleichungen der Physik, Akademische Verlagsgesellschaft Geest &Portig K.-G., Leipzig, 1962.
29. S. M. Vishik, Generalized Ray-Singer conjecture, I: A manifold with a smooth boundary, Comm. Math. Phys. 167 (1995), 1-102.
30. E. Witten, Global gravitational anomalies, Comm. Math. Phys. 100 (1985), 197-229.
31. M. Wodzicki, Spectral asymmetry and local invariants (in Russian), Habilitation thesis, Steklov Math. Inst., Moscow, 1984.
32. M. Wodzicki, “Non-commutative residue, I” in Fundamentals in K-Theory, Arithmetic and Geometry (Moscow, 1984-1986), Lecture Notes in Math. 1289, Springer-Verlag, Berlin, 1987, 320-399.
33. K. P. Wojciechowski, The additivity of the ri-invariant: The case of an invertible tangential operator, Houston J. Math. 20 (1994), 603-621.
34. K. P. Wojciechowski, The additivity of the rj-invariant: The case of a singular tangential operator, Comm. Math. Phys. 169 (1995), 315-327.