Memoirs of the American Mathematical Society 2010; 90 pp; softcover Volume: 205 ISBN10: 0821846574 ISBN13: 9780821846575 List Price: US$67 Individual Members: US$40.20 Institutional Members: US$53.60 Order Code: MEMO/205/962
 A notion of unfolding, or multiparameter deformation, of CR singularities of real submanifolds in complex manifolds is proposed, along with a definition of equivalence of unfoldings under the action of a group of analytic transformations. In the case of real surfaces in complex \(2\)space, deformations of elliptic, hyperbolic, and parabolic points are analyzed by putting the parameterdependent real analytic defining equations into normal forms up to some order. For some real analytic unfoldings in higher codimension, the method of rapid convergence is used to establish real algebraic normal forms. Table of Contents Unfolding CR singularities  Introduction
 Topological considerations
 Local defining equations and transformations
 A complexification construction
 Real surfaces in \(\mathbb{C}^2\)
 Real \(m\)submanifolds in \(\mathbb{C}^n, m < n\)
 Rapid convergence proof of the main theorem
 Some other directions
 Bibliography
