With the increased awareness among physicists and applied mathematicians
that global differential geometry and differential topology have an important
role to play in the further development of the arena of theoretical physics,
we feel it is important to inform young research physicists and mathematicians
of the problems to be formulated and solved in these applications of pure
mathematics. Consequently, a regional conference was organized and held
at the University of Pittsburgh, Pittsburgh, Pennsylvania, from July 13
through July 17, 1970. This volume contains some of the papers presented at
the Conference as well as notes on the lectures given by Professor Roger Penrose.
The manuscripts are published as supplied by the speakers, apart from changes
in format and obvious corrections.
We are grateful to the National Science Foundation for their support
of the conference (contract number GP 18904). We particularly wish to
thank Dr. Truman Botts of the Conference Board of the Mathematical Sciences
under whose auspices the Conference was organized. Thanks also go to
Miss Dolores Saylor, Mrs. Barbara Chamberlain, and Mr, Andrew R. Chopnak
for their assistance in the preparation of this volume.