Local Elliptic Boundary Value Problems for the Dirac Operator

Download or read book Local Elliptic Boundary Value Problems for the Dirac Operator written by Matthew Gregory Scholl and published by . This book was released on 2006 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two classes of local elliptic boundary conditions for the Dirac operator are studied: one posed on a family of even-dimensional spin manifolds and one posed on a family of odd-dimensional spin manifolds. It is shown that for such families of elliptic boundary value problems an associated determinant line bundle may be constructed, much as in the standard setting of a family of manifolds without boundary. The determinant line of the first class (the even problem) is shown to be isomorphic to the determinant line bundle associated to a Dirac operator on the double of the family. The second class (the odd problem) is related to the determinant line of a Dirac operator on the boundary family: we show that the squares of these determinant lines are isomorphic.