Science Mathematics

Download E-books Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold With Boundary (Memoirs of the American Mathematical Society) PDF

By P. Kirk

The topic of this memoir is the spectrum of a Dirac-type operator on an odd-dimensional manifold M with boundary and, relatively, how this spectrum varies less than an analytic perturbation of the operator. sorts of eigenfunctions are thought of: first, these gratifying the "global boundary stipulations" of Atiyah, Patodi, and Singer and moment, these which expand to $L^2$ eigenfunctions on M with an enormous collar hooked up to its boundary.

The unifying thought at the back of the research of those varieties of spectra is the proposal of yes "eigenvalue-Lagrangians" within the symplectic area $L^2(\partial M)$, an concept because of Mrowka and Nicolaescu. via learning the dynamics of those Lagrangians, the authors may be able to determine that these parts of the 2 different types of spectra which go through 0 behave in primarily an identical means (to first non-vanishing order). on occasion, this ends up in topological algorithms for computing spectral flow.

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