Memoirs of the American Mathematical Society 1996; 58 pp; softcover Volume: 124 ISBN10: 082180538X ISBN13: 9780821805381 List Price: US$38 Individual Members: US$22.80 Institutional Members: US$30.40 Order Code: MEMO/124/592
 The subject of this memoir is the spectrum of a Diractype operator on an odddimensional manifold M with boundary and, particularly, how this spectrum varies under an analytic perturbation of the operator. Two types of eigenfunctions are considered: first, those satisfying the "global boundary conditions" of Atiyah, Patodi, and Singer and second, those which extend to \(L^2\) eigenfunctions on M with an infinite collar attached to its boundary. The unifying idea behind the analysis of these two types of spectra is the notion of certain "eigenvalueLagrangians" in the symplectic space \(L^2(\partial M)\), an idea due to Mrowka and Nicolaescu. By studying the dynamics of these Lagrangians, the authors are able to establish that those portions of the two types of spectra which pass through zero behave in essentially the same way (to first nonvanishing order). In certain cases, this leads to topological algorithms for computing spectral flow. Readership Graduate students and research mathematicians interested in global analysis and analysis on manifolds. Table of Contents  Introduction
 Basics
 Eigenvalue and tangential Lagrangians
 Small extended \(L^2\)eigenvalues
 Dynamic properties of eigenvalue Lagrangians on \(N^R_\lambda\) as \(R\rightarrow \infty\)
 Properties of analytic deformations of extended \(L^2\) eigenvalues
 Time derivatives of extended \(L^2\) and APS eigenvalues
 Bibliography
