From its beginning critical point theory has been concerned with
mutual relations between topology and geometric analysis, including
differential geometry. Although it may have seemed to many to have
been directed in its initial years toward applications of topology to
analysis, one now sees that the road from topology to geometric
analysis is a two-way street. Today the methods of critical point
theory enter into the foundations of almost all studies of analysis
or geometry “in the large.��?br/>Mathematicians are finding that the study of global analysis differential topology requires a knowledge not only of the separate
techniques of analysis, differential geometry, topology, and algebra,
but also a deeper understanding of how these fields can join
forces.