Memoirs of the American Mathematical Society 1997; 80 pp; softcover Volume: 128 ISBN10: 0821806211 ISBN13: 9780821806210 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/128/609
 In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eight symmetries in the real case and two in the complex case). Readership Graduate students and research mathematicians interested in index theory; topologists and gauge theorists. Table of Contents  Algebraic preliminaries
 Topological preliminaries
 (pq)lagrangians and classifying spaces for Ktheory
 Symplectic reductions
 Clifford Symmetric Fredholm operators
 Families of boundary value problems for Dirac operators
 Appendices
 References
