Self-adjoint elliptic operators and manifold decompositions Part I: Low eigenmodes and stretching

Communications on Pure and Applied Mathematics

Volumn 49, Issue 8, 1996, Pages 825-866

  Cappell, Sylvain E ^a   Lee, Ronnie ^b   Miller, Edward Y ^c  

^a NEW YORK UNIVERSITY   (United States)

^b YALE UNIVERSITY   (United States)

^c POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030494290     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199608)49:8<825::AID-CPA3>3.3.CO;2-4     Document Type: Article

References (26)

1. Atiyah, M. F., Patodi, V. K., and Singer, I. M., Spectral asymmetry and Riemannian geometry I, Math. Proc. Camb. Phil. Soc. 77, 1975, pp. 43-69.
2. Bers, L., John, F., and Schechter, M., Partial Differential Equations, Wiley, New York, 1964.
3. Bismut, J. M., and Cheeger, J., η-invariants and their adiabatic limits, J. Amer. Math. Soc. 2, 1983, pp. 33-70.
4. Bismut, J. M., and Freed, D. S., The analysis of elliptic families: Dirac operators, eta invariants, and the holonomy theorem of Witten, Comm. Math. Phys. 107, 1986, pp. 103-163.
5. Cappell, S., Lee, R., and Miller, E., Self-adjoint elliptic operators and manifold decomposition, Part II: Spectral flow and Maslov index, Comm. Pure Appl. Math., 1996, in press.
6. Cappell, S., Lee, R., and Miller, E., Self-adjoint elliptic operators and manifold decomposition, Part III: Applications to Casson's invariant, to appear.
7. Cappell, S., Lee, R., and Miller, E., On the Maslov index, Comm. Pure Appl. Math. 67, 1994, pp. 121-186.
8. Chavel, I., Eigenvalues in Riemannian Geometry, Pure and Applied Mathematics No. 115, Academic Press, Orlando, Fla., 1984.
9. Cheeger, J., Spectral geometry of spaces with cone-tike singularities, Proc. Nat. Acad. Sci. U.S.A. 76(5), 1979, pp. 2103-2106.
10. Cheeger, J., On the Hodge theory of Riemannian pseudomanifolds, pp. 91-146 in: Geometry of the Laplace Operator (Proceedings of the Symposium on Pure Mathematics, University of Hawaii, Honolulu, Hawaii, 1979), American Mathematical Society, Providence, R.I., 1980.
11. Cheeger, J., η-invariant, the adiabatic approximation and conical singularities, J. Differential Geom. 26, 1987, pp. 175-221.
12. Cheeger, J., Spectral geometry of singular Riemannian spaces, J. Differential Geom. 18, 1983, pp. 575-657.
13. Dai, X., The Adiabatic Limit, Non-multiplicativity of the Leray Spectral Sequence, Doctoral Dissertation, State University of New York at Stony Brook, 1989.
14. Douglas, R., and Wojciechowski, K. P., Adiabatic limits of η-invariants. The odd-dimensional Atiyah-Patodi-Singerproblem., Comm. Math. Phys. 42, 1991, pp. 139-168.
15. Hirzebruch, F., Topological Methods in Algebraic Geometry, Classics in Mathematics, Springer-Verlag, New York, 1966.
16. Kato, T., Perturbation Theory for Linear Operators, Grundlehren der Mathematischen Wissenschaften 132, Springer-Verlag, New York, 1980.
17. Masseo, R., and Melrose, R., The adiabatic limit, Hodge cohomology, and Leray's spectral sequence for a fibration, J. Differential Geom. 31, 1990, pp. 185-213.
18. Mrowka, T., Mayer-Vietoris Decompositions in Gauge Theory, Doctoral Dissertation, U. C. Berkeley, 1989.
19. 2-lndex Theorem, Lecture Notes in Mathematics No. 1244, Springer-Verlag, New York-Berlin, 1987.
20. Palais, R. S., Seminar on the Atiyah-Singer Index Theorem, Annals of Mathematical Studies No. 57, Princeton University Press, Princeton, N.J., 1965.
21. Taubes, C. H., The stable topology of Yang-Mills moduli spaces, J. Differential Geom. 29, 1989, pp. 163-230.
22. Taubes, C. H., Casson's invariant and gauge theory, J. Differential Geom. 31, 1990, pp. 547-599.
23. Witten, E., Global gravitational anomalies, Comm. Math. Phys. 100, 1985, pp. 197-229.
24. Wojciechowski, K. P., Elliptic operators and relative K-homology groups on manifolds with boundary, C. R. Math. Rep. Acad. Sci. Canada 7, 1985, pp. 149-154.
25. Wojciechowski, K. P., On the Calderon projections and spectral projections of elliptic operators, J. Operator Theory 20, 1988, pp. 107-115.
26. Yoshida, T., Floer homology and splittings of manifolds, Ann. of Math. (2) 134, 1991, pp. 277-323.