In August 1993 a meeting was held in Cocoyoc, Mexico on the subject of
Homotopy Theory and its Applications. There were many foreign participants
in addition to a number of Mexican topologists. The main focus of the meeting
was to highlight the current development of methods in homotopy theory, and
how they can be applied to interesting problems involving classifying spaces,
moduli spaces, representation theory, etc. The 16 papers in this volume testify
to the diversity and activity in this area of mathematics.
This conference was partly held to celebrate Samuel Gitler's sixtieth birth-
day. Gitler studied mathematics and engineering at the National University of
Mexico (UNAM) before doing his graduate studies at Princeton University un-
der Norman Steenrod, obtaining his Ph. D. in 1960. Soon after he was invited
by Jose Adem to join the faculty at the newly created Centro de Investigaci6n
y de Estudios A vanzados del Instituto Politecnico N acional. Adem and Gitler
created a unique atmosphere of high level research in mathematics at the Cen-
tro, and many mathematicians remember Sam's hospitality and mathematical
collaboration with great fondness. Gitler's research has been highly regarded
for many years, and it involves many aspects of topology, especially homotopy
theory. Perhaps his best known work was the description that he and Ed Brown
gave of the so-called Brown-Gitler spectra, which have played an important role
in algebraic topology over the past two decades. Gitler has had many collab-
orators over the years, including Adem, Astey, Antoniano, Bendersky, Berrick,
Boyer, Brown, Davis, Feder, Iberkleid, Handel, James, Lam, Mahowald, Micha,
Milgram, Pastor, Stasheff, Ucci, Verjovsky and Zvengrovsky.
Sam Gitler has contributed significantly to the development of mathematics in
Mexico. He served as editor of the Boletin de la Sociedad Matematica Mexicana
and ran many seminars which helped to educate young topologists in Mexico. In
recognition of his contributions to mathematics in Mexico, Gitler was awarded
the National Science Prize in 1976 by the Mexican government, and in 1986 he
was elected a member of the prestigious Colegio N acional.
Since 1987 Sam Gitler has been at the University of Rochester, where he
helped to assemble one of the leading research groups in homotopy theory. We
are sure that Sam has many productive years ahead of him, and it is a great
pleasure for us to dedicate this volume to him.