An Extension of a Theorem of Nicolaescu on Spectral Flow and the Maslov Index

The Maslov Index , the Spectral Flow , and Decompositions of Manifolds

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

The h-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary

Several proofs have been published of the modZ gluing formula for the h-invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the h-invariant is left obscure in the literature. In this article we present a gluing formula for the h-invariant which expresses the integer contribution as a triple index involving the boundary conditions and the Calderón pr...

The η–invariant, Maslov index, and spectral flow for Dirac–type operators on manifolds with boundary

Several proofs have been published of the modZ gluing formula for the η–invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the η–invariant is left obscure in the literature. In this article we present a gluing formula for the η–invariant which expresses the integer contribution as a triple index involving the boundary conditions and the Calderón pr...

A Generalized Index Theorem for Morse-sturm Systems and Applications to Semi-riemannian Geometry

We prove an extension of the Index Theorem for Morse–Sturm systems of the form −V ′′ + RV = 0, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint. The result is then applied to the case of a Jacobi equation along a geodesic in a Lorentzian manifold, obtaining an extension of the Morse Index Theorem ...