# Computation of the Maslov index and the spectral flow via partial signatures

@article{Giamb2004ComputationOT,
title={Computation of the Maslov index and the spectral flow via partial signatures},
author={Roberto Giamb{\o} and Paolo Piccione and Alessandro Portaluri},
journal={Comptes Rendus Mathematique},
year={2004},
volume={338},
pages={397-402}
}`
• Published 1 March 2004
• Mathematics
• Comptes Rendus Mathematique
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## References

SHOWING 1-10 OF 14 REFERENCES
Jumps of the eta-invariant
• Mathematics
• 1994
We study the eta-invariant, defined by Atiyah-Patodi-Singer a real valued invariant of an oriented odd-dimensional Riemannian manifold equipped with a unitary representation of its fundamental group.
Self-adjoint Fredholm operators and spectral flow
Abstract We study the topology of the nontrivial component, , of self-adjoint Fredholm operators on a separable Hilbert space. In particular, if {Bt } is a path of such operators, we can associate to
The spectral flow of the odd signature operator and higher Massey products
• Mathematics
• 1994
We show how to compute the spectral flow of the odd signature operator $\pm *d_{a_t}-d_{a_t}*$ along an analytic path of flat connections $a_t$ on a bundle over a closed odd-dimensional manifold in
The Weil Representation
There is a whole aspect of SL 2(R) into which we shall not go, namely the various models which can be found in an infinitesimal equivalence class of representations, and the possibility of finding
Gosson,La relation entreSp∞, rev̂etement universel du groupe symplectique, et Sp × Z, andLe définition de l’indice de Maslov sans hypoth èse de transversalit é
• C. R. Acad. Sci. Paris,
• 1990
E
• Klassen,The spectral flow of the odd signature operator and higher Massey products , Math. Proc. Cambridge Philos. Soc. 121
• 1997