# 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} }

## 32 Citations

On the Maslov index of symplectic paths that are not transversal to the Maslov cycle. Semi-Riemannian index theorems in the degenerate case

- Mathematics
- 2003

We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a…

ON THE MASLOV INDEX OF LAGRANGIAN PATHS THAT ARE NOT TRANSVERSAL TO THE MASLOV CYCLE. SEMI-RIEMANNIAN INDEX THEOREMS IN THE DEGENERATE CASE

- Mathematics
- 2003

The Maslov index of a Lagrangian path, under a certain trans versality assumption, is given by an algebraic count of the intersection s f the path with a subvariety of the Lagrangian Grassmannian…

Spectral Flow, Maslov Index and Bifurcation of Semi-Riemannian Geodesics

- Mathematics
- 2002

We give a functional analytical proof of the equalitybetween the Maslov index of a semi-Riemannian geodesicand the spectral flow of the path of self-adjointFredholm operators obtained from the index…

On a formula for the spectral flow and its applications

- Mathematics
- 2008

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms…

Iteration of closed geodesics in stationary Lorentzian manifolds

- Mathematics
- 2007

Following the lines of Bott in (Commun Pure Appl Math 9:171–206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a…

Instability of semi-Riemannian closed geodesics

- MathematicsNonlinearity
- 2019

A celebrated result due to Poincare affirms that a closed non-degenerate minimizing geodesic $\gamma$ on an oriented Riemannian surface is hyperbolic. Starting from this classical theorem, our first…

Sturm theory with applications in geometry and classical mechanics

- Mathematics
- 2020

Classical Sturm non-oscillation and comparison theorems as well as the Sturm theorem on zeros for solutions of second order differential equations have a natural symplectic version, since they…

Linear instability for periodic orbits of non-autonomous Lagrangian systems

- Mathematics
- 2019

Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the…

## 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

- Mathematics
- 1996

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

- Mathematics
- 1985

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