The Maslov index, the spectral flow, and decompositions of manifolds

previous :: next

The Maslov index, the spectral flow, and decompositions of manifolds

Liviu I. Nicolaescu

Source: Duke Math. J. Volume 80, Number 2 (1995), 485-533.

First Page: Show

Primary Subjects: 58G10

Secondary Subjects: 57R57, 58F05, 58G25

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077246090
Mathematical Reviews number (MathSciNet): MR1369400
Zentralblatt MATH identifier: 0849.58064
Digital Object Identifier: doi:10.1215/S0012-7094-95-08018-1

back to Table of Contents

References

[Ar] V. I. Arnold, Une classe charactéristique intervenant dans les conditions de quantification, Dunod, Paris, 1972, appendix to Théorie des perturbations et methodes asymptotiques.

[APS1] 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.

Mathematical Reviews (MathSciNet): MR53:1655a

Zentralblatt MATH: 0297.58008

Digital Object Identifier: doi:10.1017/S0305004100049410

[APS2] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. II, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 3, 405–432.

Mathematical Reviews (MathSciNet): MR53:1655b

Zentralblatt MATH: 0314.58016

Digital Object Identifier: doi:10.1017/S0305004100051872

[APS3] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. III, Math. Proc. Cambridge Philos. Soc. 79 (1976), no. 1, 71–99.

Mathematical Reviews (MathSciNet): MR53:1655c

Zentralblatt MATH: 0325.58015

Digital Object Identifier: doi:10.1017/S0305004100052105

[AS] M. F. Atiyah and I. M. Singer, Index theory for skew-adjoint Fredholm operators, Inst. Hautes Études Sci. Publ. Math. (1969), no. 37, 5–26.

Mathematical Reviews (MathSciNet): MR44:2257

Zentralblatt MATH: 0194.55503

Digital Object Identifier: doi:10.1007/BF02684885

[B] B. Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986.

Mathematical Reviews (MathSciNet): MR88g:46082

Zentralblatt MATH: 0597.46072

[BGV] N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 298, Springer-Verlag, Berlin, 1992.

Mathematical Reviews (MathSciNet): MR94e:58130

Zentralblatt MATH: 0744.58001

[BW1] B. Booss and K. Wojciechowski, Desuspension of splitting elliptic symbols. I, Ann. Global Anal. Geom. 3 (1985), no. 3, 337–383.

Mathematical Reviews (MathSciNet): MR87f:58148

Zentralblatt MATH: 0599.58041

Digital Object Identifier: doi:10.1007/BF00130485

[BW2] B. Booss and K. Wojciechowski, Desuspension of splitting elliptic symbols. II, Ann. Global Anal. Geom. 4 (1986), no. 3, 349–400.

Mathematical Reviews (MathSciNet): MR89f:58126

Zentralblatt MATH: 0624.58026

Digital Object Identifier: doi:10.1007/BF00128052

[BW3] B. Booss-Bavnbek and K. Wojciechowski, Pseudo-differential projections and the topology of certain spaces of elliptic boundary value problems, Comm. Math. Phys. 121 (1989), no. 1, 1–9.

Mathematical Reviews (MathSciNet): MR90b:58263

Zentralblatt MATH: 0683.58044

Digital Object Identifier: doi:10.1007/BF01218620

Project Euclid: euclid.cmp/1104177999

[BW4] B. Booss and K. Wojciechowski, Elliptic boundary problems for Dirac operators, Mathematics: Theory & Applications, Birkhäuser Boston Inc., Boston, MA, 1993.

Mathematical Reviews (MathSciNet): MR94h:58168

Zentralblatt MATH: 0797.58004

[Bu1] U. Bunke, A glueing formula for the $\eta$-invariant, preprint, Humboldt-Universitat, Berlin, 1993.

[Bu2] U. Bunke, Splitting the spectral flow, preprint, Humboldt-Universitat, Berlin, 1993.

[CLM1] S. Capell, R. Lee, and E. Y. Miller, On the Maslov index, preprint.

[CLM2] S. Capell, R. Lee, and E. Y. Miller, Selfadjoint elliptic operators and manifold decomposition Part I: Low eigenvalues and stretching, preprint.

[C] H. O. Cordes, Elliptic pseudodifferential operators—an abstract theory, Lecture Notes in Mathematics, vol. 756, Springer, Berlin, 1979.

Mathematical Reviews (MathSciNet): MR81j:47041

Zentralblatt MATH: 0417.35004

[D1] J. J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences New York University, New York, 1973.

Mathematical Reviews (MathSciNet): MR56:9600

Zentralblatt MATH: 0272.47028

[D2] J. J. Duistermaat, On the Morse index in variational calculus, Advances in Math. 21 (1976), no. 2, 173–195.

Mathematical Reviews (MathSciNet): MR58:31190

Zentralblatt MATH: 0361.49026

Digital Object Identifier: doi:10.1016/0001-8708(76)90074-8

[DP] P. Dazord and G. Patissier, La première classe de Chern comme obstruction à la quantification asymptotique, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) eds. P. Dazord and A. Weinstein, Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 73–97.

Mathematical Reviews (MathSciNet): MR92k:58091

Zentralblatt MATH: 0732.58020

[DRS] S. Dostoglou, J. W. Robin, and D. Salamon, The spectral flow and the Maslov index, preprint.

[F] A. Floer, A relative Morse index for the symplectic action, Comm. Pure Appl. Math. 41 (1988), no. 4, 393–407.

Mathematical Reviews (MathSciNet): MR89f:58055

Zentralblatt MATH: 0633.58009

Digital Object Identifier: doi:10.1002/cpa.3160410402

[GS] V. Guillemin and S. Sternberg, Geometric asymptotics, American Mathematical Society, Providence, R.I., 1977.

Mathematical Reviews (MathSciNet): MR58:24404

Zentralblatt MATH: 0364.53011

[Kar] M. Karoubi, $K$-Theory: An Introduction, Springer-Verlag, Berlin, 1977.

Mathematical Reviews (MathSciNet): MR2458205

[K] T. Kato, Perturbation Theory for Linear Operators, 2d ed., Springer-Verlag, Berlin, 1984.

Zentralblatt MATH: 0531.47014

[Ku] N. Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965), 19–30.

Mathematical Reviews (MathSciNet): MR31:4034

Zentralblatt MATH: 0129.38901

Digital Object Identifier: doi:10.1016/0040-9383(65)90067-4

[LiMa] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968.

Mathematical Reviews (MathSciNet): MR40:512

Zentralblatt MATH: 0165.10801

[N1] L. I. Nicolaescu, The Maslov index, the spectral flow and splittings of manifolds, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 5, 515–519.

Mathematical Reviews (MathSciNet): MR94k:58148

Zentralblatt MATH: 0780.58021

[N2] L. I. Nicolaescu, The index of families of boundary value problems for Dirac operators, preprint, 1994 (announced in C.R. Acad. Sci. Paris Sér. I Math. 320(1995), 347–352).

Mathematical Reviews (MathSciNet): MR1320383

[N3] L. I. Nicolaescu, Morse theory on Grassmanians, to appear in Anal. Sti. Univ. Iasi.

Mathematical Reviews (MathSciNet): MR1328945

[P1] R. S. Palais, On the homotopy type of certain groups of operators, Topology 3 (1965), 271–279.

Mathematical Reviews (MathSciNet): MR30:5315

Zentralblatt MATH: 0161.34501

Digital Object Identifier: doi:10.1016/0040-9383(65)90057-1

[P2] R. S. Palais, Seminar on the Atiyah-Singer index theorem, With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965.

Mathematical Reviews (MathSciNet): MR33:6649

Zentralblatt MATH: 0137.17002

[RS] J. Robbin and D. Salamon, The Maslov index for paths, Topology 32 (1993), no. 4, 827–844.

Mathematical Reviews (MathSciNet): MR94i:58071

Zentralblatt MATH: 0798.58018

Digital Object Identifier: doi:10.1016/0040-9383(93)90052-W

[S] R. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781–809.

Mathematical Reviews (MathSciNet): MR35:810

Zentralblatt MATH: 0178.17601

Digital Object Identifier: doi:10.2307/2373078

JSTOR: links.jstor.org

[V] C. Viterbo, Intersection de sous-variétés lagrangiennes, fonctionnelles d'action et indice des systèmes hamiltoniens, Bull. Soc. Math. France 115 (1987), no. 3, 361–390.

Mathematical Reviews (MathSciNet): MR89b:58081

Zentralblatt MATH: 0639.58018

[W] K. Wojciechowski, A note on the space of pseudodifferential projections with the same principal symbol, J. Operator Theory 15 (1986), no. 2, 207–216.

Mathematical Reviews (MathSciNet): MR87i:58011

Zentralblatt MATH: 0615.47039

[Y] T. Yoshida, Floer homology and splittings of manifolds, Ann. of Math. (2) 134 (1991), no. 2, 277–323.

Mathematical Reviews (MathSciNet): MR92m:57041

Zentralblatt MATH: 0748.57002

Digital Object Identifier: doi:10.2307/2944348

JSTOR: links.jstor.org

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?