The papers in these Proceedings grew out of lectures given at the fifteenth
Summer Mathematical Institute of the American Mathematical Society, whose
topic was global analysis. The Institute was held at the University of California
at Berkeley from July 1 to July 26,1968, and was partiallyfinancedby the National
Notes of lectures were distributed at the time of the conference and some of the
papers here arejust as in those notes. These volumes, however, can be distinguished
from the notes in the sense that in general the papers here are not just expositions
of material that has or will appear elsewhere; most of the articles could just as well
have appeared in Journals.
The unity given by the subject matter makes it desirable to collect them here.
It is hoped that the volumes will provide an important start to the scientist who
wishes to learn what is going on in that part of mathematics called global analysis.
The organizing committee for the institute consisted of: F. Browder,
S.-S. Chern, L. Hormander, I. Singer, and S. Smale, with the co-editors serving
Seminar organizers were: F. Browder, E. Calabi, H. Goldschmidt, R. Hermann,
C. Morrey, R. Palais, C. Pugh, I. Singer, and D. Spencer.
Finally the editors would like to thank the many people who made the institute
and volumes possible. Of especially direct help to ourselves were Celeste Andrade,
Ann Harrington, Gordon and Jacqueline Walker.