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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 98081, 16 pages
http://dx.doi.org/10.1155/AAA/2006/98081

Surgery and the relative index in elliptic theory

1Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101-1, Moscow 119526, Russia
2Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, Moscow 119002, Russia

Received 26 June 2005; Accepted 1 July 2005

Copyright © 2006 V. E. Nazaikinskii and B. Yu. Sternin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. S. Agranovich, “Elliptic boundary problems,” in Partial Differential Equations, IX, vol. 79 of Encyclopaedia Math. Sci., pp. 1–144, 275–281, Springer, Berlin, 1997. View at Zentralblatt MATH · View at MathSciNet
  2. M. S. Agranovich and A. S. Dynin, “General boundary-value problems for elliptic systems in higher-dimensional regions,” Doklady Akademii Nauk SSSR, vol. 146, pp. 511–514, 1962. View at Zentralblatt MATH · View at MathSciNet
  3. N. Anghel, “An abstract index theorem on noncompact Riemannian manifolds,” Houston Journal of Mathematics, vol. 19, no. 2, pp. 223–237, 1993. View at Zentralblatt MATH · View at MathSciNet
  4. M. F. Atiyah, “Global theory of elliptic operators,” in Proceedings of the International Symposium on Functional Analysis, pp. 21–30, University of Tokyo Press, Tokyo, 1969.
  5. M. F. Atiyah and R. Bott, “The index problem for manifolds with boundary,” in Differential Analysis, Bombay Colloquium, pp. 175–186, Oxford University Press, London, 1964. View at Zentralblatt MATH · View at MathSciNet
  6. Yu. V. Egorov and B.-W. Schulze, Pseudo-differential operators, singularities, applications, vol. 93 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 1997. View at Zentralblatt MATH · View at MathSciNet
  7. C. Epstein and R. Melrose, “Contact degree and the index of Fourier integral operators,” Mathematical Research Letters, vol. 5, no. 3, pp. 363–381, 1998. View at Zentralblatt MATH · View at MathSciNet
  8. M. Gromov and H. B. Lawson, Jr., “Positive scalar curvature and the Dirac operator on complete Riemannian manifolds,” Institut des Hautes Études Scientifiques. Publications Mathématiques, vol. 58, pp. 83–196 (1984), 1983. View at Zentralblatt MATH · View at MathSciNet
  9. E. Leichtnam, R. Nest, and B. Tsygan, “Local formula for the index of a Fourier integral operator,” Journal of Differential Geometry, vol. 59, no. 2, pp. 269–300, 2001. View at Zentralblatt MATH · View at MathSciNet
  10. V. P. Maslov, Théorie des Perturbations et Méthod Asymptotiques, Dunod, Paris, 1972, French translation from the Russian 1965 edition.
  11. R. B. Melrose, “Transformation of boundary problems,” Acta Mathematica, vol. 147, no. 3-4, pp. 149–236, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. S. Mishchenko, V. E. Shatalov, and B. Yu. Sternin, Lagrangian Manifolds and the Maslov Operator, Springer Series in Soviet Mathematics, Springer, Berlin, 1990. View at Zentralblatt MATH · View at MathSciNet
  13. V. E. Nazaikinskii, A. Savin, B.-W. Schulze, and B. Yu. Sternin, Elliptic Theory on Singular Manifolds, CRC-Press, Florida, 2005.
  14. V. E. Nazaikinskii and B. Yu. Sternin, “Localization and surgery in index theory of elliptic operators,” in Conference: Operator Algebras and Asymptotics on Manifolds with Singularities, pp. 27–28, Stefan Banach International Mathematical Center, Universität Potsdam, Institut für Mathematik, Warsaw, 1999.
  15. V. E. Nazaikinskii and B. Yu. Sternin, “A remark on elliptic theory on manifolds with isolated singularities,” Rossiĭskaya Akademiya Nauk. Doklady Akademii Nauk, vol. 374, no. 5, pp. 606–610, 2000. View at Zentralblatt MATH · View at MathSciNet
  16. V. E. Nazaikinskii and B. Yu. Sternin, “Localization and surgery in the index theory to elliptic operators,” Russian Mathematics. Doklady, vol. 370, no. 1, pp. 19–23, 2000.
  17. V. E. Nazaikinskii and B. Yu. Sternin, “On the local index principle in elliptic theory,” Functional Analysis and Its Applications, vol. 35, no. 2, pp. 111–123, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  18. V. E. Nazaikinskii and B. Yu. Sternin, “Surgery and the relative index in elliptic theory,” University of Potsdam, Institut für Mathematik, preprint N 99/17, Juli 1999.
  19. B.-W. Schulze, B. Yu. Sternin, and V. E. Shatalov, “On the index of differential operators on manifolds with conical singularities,” Annals of Global Analysis and Geometry, vol. 16, no. 2, pp. 141–172, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A. Weinstein, “Fourier integral operators, quantization, and the spectra of Riemannian manifolds,” in Géométrie symplectique et physique mathématique (Colloq. Internat. CNRS, No. 237, Aix-en-Provence, 1974), pp. 289–298, Éditions Centre Nat. Recherche Sci., Paris, 1975. View at Zentralblatt MATH · View at MathSciNet
  21. A. Weinstein, “Some questions about the index of quantized contact transformations,” Sūrikaisekikenkyūsho Kōkyūroku, no. 1014, pp. 1–14, 1997. View at Zentralblatt MATH · View at MathSciNet