An extension of a theorem of Nicolaescu on spectral flow and the Maslov index
HTML articles powered by AMS MathViewer
- by Mark Daniel
- Proc. Amer. Math. Soc. 128 (2000), 611-619
- DOI: https://doi.org/10.1090/S0002-9939-99-05002-9
- Published electronically: July 28, 1999
- PDF | Request permission
Abstract:
In this paper we extend a theorem of Nicolaescu on spectral flow and the Maslov index. We do this by studying the manifold of Lagrangian subspaces of a symplectic Hilbert space that are Fredholm with respect to a given Lagrangian $L_0$. In particular, we consider the neighborhoods in this manifold of Lagrangians which intersect $L_0$ nontrivially.References
- Sylvain E. Cappell, Ronnie Lee, and Edward Y. Miller, Self-adjoint elliptic operators and manifold decompositions. I. Low eigenmodes and stretching, Comm. Pure Appl. Math. 49 (1996), no. 8, 825–866. MR 1391757, DOI 10.1002/(SICI)1097-0312(199608)49:8<825::AID-CPA3>3.3.CO;2-4
- Sylvain E. Cappell, Ronnie Lee, and Edward Y. Miller, Self-adjoint elliptic operators and manifold decompositions. II. Spectral flow and Maslov index, Comm. Pure Appl. Math. 49 (1996), no. 9, 869–909. MR 1399200, DOI 10.1002/(SICI)1097-0312(199609)49:9<869::AID-CPA1>3.0.CO;2-5
- Sylvain E. Cappell, Ronnie Lee, and Edward Y. Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994), no. 2, 121–186. MR 1263126, DOI 10.1002/cpa.3160470202
- A.M.Daniel, Maslov index, symplectic reduction in a symplectic Hilbert space and a splitting formula for spectral flow, Doctoral Dissertation, Indiana University, Bloomington, 1997.
- Tosio Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1980 edition. MR 1335452
- P. Kirk and E. Klassen, Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary, Mem. Amer. Math. Soc. 124 (1996), no. 592, viii+58. MR 1355034, DOI 10.1090/memo/0592
- Liviu I. Nicolaescu, The Maslov index, the spectral flow, and decompositions of manifolds, Duke Math. J. 80 (1995), no. 2, 485–533. MR 1369400, DOI 10.1215/S0012-7094-95-08018-1
Bibliographic Information
- Mark Daniel
- Affiliation: Applied Physics Operation, SAIC, McLean, Virginia 22102
- Address at time of publication: Advanced Power Technologies, Inc., 1250 Twenty-Fourth St., NW, Suite 850, Washington, DC 20037
- Email: amdaniel@ccf.nrl.navy.mil, amdaniel@apti.com
- Received by editor(s): January 20, 1998
- Received by editor(s) in revised form: April 7, 1998
- Published electronically: July 28, 1999
- Communicated by: Ronald A. Fintushel
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 611-619
- MSC (1991): Primary 57M99; Secondary 53C15, 58G25
- DOI: https://doi.org/10.1090/S0002-9939-99-05002-9
- MathSciNet review: 1622789