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An extension of a theorem of Nicolaescu on spectral flow and the Maslov index
Author(s):
Mark
Daniel
Journal:
Proc. Amer. Math. Soc.
128
(2000),
611-619.
MSC (1991):
Primary 57M99;
Secondary 53C15, 58G25
Posted:
July 28, 1999
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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  . In particular, we consider the neighborhoods in this manifold of Lagrangians which intersect  nontrivially.
References:
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- 2.
- S.Cappell, R.Lee, & E.Miller, Self-adjoint elliptic operators and manifold decompositions, Part II: Spectral flow and Maslov index, Comm. Pure Appl. Math 49 (1996), 869-909. MR 97g:58163
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- S.Cappell, R.Lee, & E.Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994), 121-186. MR 95f:57045
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- 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.
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- P.Kirk & 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), number 592.MR 97d:58184
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Additional 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
DOI:
10.1090/S0002-9939-99-05002-9
PII:
S 0002-9939(99)05002-9
Keywords:
Spectral flow,
Maslov index,
Lagrangian subspace
Received by editor(s):
January 20, 1998
Received by editor(s) in revised form:
April 7, 1998
Posted:
July 28, 1999
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
1999,
American Mathematical Society
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