A major international meeting on homotopy theory took place in
Kinosaki, Japan, from July 28–August 1 2003, followed on August
4–8 by an intense satellite conference at the Nagoya Institute
of Technology. This volume contains the Proceedings of those
conferences. They, and this volume, are dedicated to Professor
Gôrô Nishida on the occasion of his 60th birthday.
Nishida's earliest work grew out of the study of infinite
loopspaces. His first paper (in 1968, on what came eventually to be
known as the Nishida relations) accounts for interactions between
Steenrod and Dyer–Lashof (Kudo–Araki) operations. This
was followed by early work with H Toda on the extended power
construction, which led in 1973 to his milestone proof of the
nilpotence of positive-degree elements in the stable homotopy ring
of spheres.
This result, whose echoes continue to reverberate today in work of
Devinatz, Hopkins, Smith, and others on the chromatic picture, and
in work on motives in algebraic geometry, stood at the time as an
isolated beacon of hope in the (then very mysterious) world of stable
homotopy theory. It, together with the Kahn-Priddy theorem, was one
of the first signs that the subject possesses deep global
properties – that it held structural secrets well beyond its
already formidable computational aspects. Nishida next turned his
attention to a circle of ideas surrounding the Segal conjecture,
transfer homomorphisms, and stable splittings of classifying
spaces of groups. The ideas in this series of papers have by
now grown into a rich subfield of homotopy theory, with important
contributions by Benson, Feshbach, Martino, Minami, Priddy, Webb,
and many others; it continues today in (for example) the theory of
p-compact groups. In recent years much of his work has been concerned
with various aspects of elliptic cohomology. His deep insight from
the early 90's, that work of Eichler and Shimura on modular forms,
higher S1–transfers, and the diffeomorphism group of
the two-torus are all intimately connected, is still not adequately
understood; its exploitation may depend on new geometric ideas from
the developing theory of elliptic objects.
Today in retrospect Nishida's thinking has always seemed very
global and adventuresome – as he has been, personally, as well
– reaching back at least as far as his early 70's postdoc in
Manchester. His hospitality and kindness to visitors is legendary,
and he has devoted enormous energies to opening the international
community to younger researchers. This volume is dedicated to him
by his many colleagues, in recognition of and admiration for his
ideas and his work.
The NSF supported travel to this conference by more than twenty
researchers from the US, under grant DMS 0080657; it was the greatest
opportunity in a generation for younger algebraic topologists on
both sides of the Pacific to confer about common interests. The
conferences focused on the broad range of subjects which Professor
Nishida has influenced, and which are still critical to research
today: localization, periodicity in homotopy theory, higher
K–theories, infinite loop spaces, homology and cohomology
operations, modular forms, group cohomology, and stable homotopy of
classifying spaces. The organizing committee on the Japanese side
was headed by Professor Norihiko Minami of the Nagoya Institute of
Technology (representing Professor Kazuhisa Shimakawa of Okayama
University), assisted by Atsushi Yamaguchi of Osaka Prefecture
University, Akihiro Oshita of the Osaka University of Economics,
Dai Tamaki of Shinshu University, and Hirofumi Nakai of the Oshima
College of Maritime Technology. Stewart Priddy of Northwestern,
Jack Morava and W Stephen Wilson of Johns Hopkins, and Clarence
Wilkerson of Purdue were the organizing committee on the US side.
The Editors
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