On the η-invariant of generalized Atiyah-Patodi-Singer boundary value problems

Illinois Journal of Mathematics

Volumn 40, Issue 1, 1996, Pages 30-46

  Lesch, Matthias ^a   Wojciechowski, Krzysztof P ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030092741     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1255986187     Document Type: Article

References (21)

1. M. F. ATIYAH, V. K. PATODI, and I. M. SINGER, Spectral asymmetry and Riemannian Geometry I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43-69.
2. B. BOOSS and K. P. WOJCIECHOWSKI, Pseudodifferential projections and the topology of certain spaces of elliptic boundary value problems. Comm.Math. Phys. 121 (1989), 1-9.
3. _, Elliptic boundary problems for Dirac operators, Birkhäuser, to appear.
4. T. BRANSON and P GILKEY, Residues of the eta-function for an operator of Dirac type, J. Funct. Anal. 108 (1992), 47-87.
5. U. BUNKE, A glueing formula for the η-invariant, preprint, 1993.
6. J. CHEEGER, η-invariants, the adiabatic approximation and conical singularities, J. Differential Geom. 26 (1987), 175-221
7. _, Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18 (1983), 575-657.
8. P. R. CHERNOFF, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401-414.
9. R. G. DOUGLAS and K. P. WOJCIECHOWSKI, Adiabatic limits of the η-invariants: the odd-dimensional Atiyah-Patodi-Singer problem, Comm. Math. Phys. 142 (1991), 139-168.
10. K. FURUTANI and N. OTSUKI, Spectral flow and intersection number, J. Math. Kyoto Univ. 33 (1993), 261-283.
11. P. GILKEY, Invariance theory, the heat equation, and the Atiyah-Singer index theorem, Publish or Perish, Wilmington, DE, 1984.
12. M. GROMOV and H. B. LAWSON, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 83-196.
13. N. HIGSON, A note on the cobordism invariance of the index, Topology 30 (1991), 439-443.
14. S. KLIMEK and K. P. WOJCIECHOWSKI, η-invariants on the manifolds with cylindrical ends, Differential Geometry and Applications, to appear.
15. M. LESCH, Deficiency indices for symmetric Dirac operators on manifolds with conical singularities, Topology 32 ( 1993), 611-623.
16. _, On a class of singular differential operators and asymptotic methods, Habilitationss-chrift, Augsburg, June 1993.
17. H. B. LAWSON and M. L. MICHELSOHN, Spin geometry, Princeton University Press, Princeton N.J., 1989.
18. W. MÜLLER, η-invariants and manifolds with boundary, preprint, 1993.
19. L. NICOLAESCU, The Maslov index, the spectral flow and splittings of manifolds, in preparation.
20. R. S. PALAIS, Seminar on the Atiyah-Singer index theorem, Ann. of Math. Studies, Princeton Univ. Press, Princeton, N.J., 1965.
21. K. P. WOJCIECHOWSKI, On the additivity the η-invariant, preprint, 1993.