Continuity and analyticity of families of self-adjoint Dirac operators on a manifold with boundary

Illinois Journal of Mathematics

Volumn 42, Issue 1, 1998, Pages 123-138

  Kirk, P ^a   Klassen, E ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039401915     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1255985617     Document Type: Article

References (16)

1. M. Atiyah, V. Patodi, and I. Singer, Spectral asymmetry and Riemanian geometry, I, II, III, Math. Proc. Cambridge Philos. Soc. 77, 78, 79 (1975).
2. J. M. Bismuth and J. Cheeger, Families index for manifolds with boundary, superconnections and cones I, J. Funct. Anal. 89 (1990), 313-363.
3. B. Booss-Bavnbek and K. Wojciechowski, Elliptic boundary problems for Dirac operators, Birkhauser, 1993.
4. U. Bunke, On the spectral flow of families of Dirac operators with constant symbol, Math. Nachr. 165 (1994), 191-203.
5. S. Cappell, R. Lee, and E. Miller, Self-adjoint elliptic operators and manifold decompositions. II. Spectral flow and Maslov index. Comm. Pure Appl. Math. 49 (1996), no. 9, 869-909.
6. M. Farber and J. Levine, Jumps of the eta-invariant. With an appendix by Shmuel Weinberger: Rationality of ρ-invariants, Math. Z. 223 (1996), no. 2, 197-246.
7. T. Kato, Perturbation theory for linear operators, Grundlehren der Mathematischen Wissenschaft, no. 132, Springer-Verlag, 1966.
8. P. Kirk and E. Klassen, Computing spectral flow via cup products, J. Differential Geometry 40 (1994), 505-562.
9. _, The spectral flow of the odd signature operator and higher Massey products, Math. Proc. Cambridge Philos. Soc. 121 (1997), 297-320.
10. _, Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary, Mem. Amer. Math. Soc. 124(592), (1996).
11. R. Melrose and P. Piazza, Families of Dirac operators, boundaries and the b-calculus, preprint, 1995.
12. T. Mrowka and K. Walker, notes, 1990.
13. L. Nicolaescu, The Maslov index, the spectral flow, and splittings of manifolds, Duke Math. J. 80(2) (1995), 485-533.
14. R. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, no. 57, Princeton University Press, 1965.
15. C. Taubes, Casson's invariant and gauge theory, J. Differential Geometry 31 (1990), 547-599.
16. T. Yoshida, Floer homology and splittings of manifolds, Ann. of Math. 143 (1991), 277-324.