A BRIEF INTRODUCTION TO THE WORK OF
J.PETER MAY, ON THE OCCASION OF HIS 60TH
BIRTHDAY
IGOR KRIZ
1.
INTRODUCTION
This paper is essentially a transcript of a talk I gave at the Boulder
conference. Its inadequacy will be obvious: it is almost impossible to
describe work as broad as Peter's (work which is still very much in
progress) in a lecture or article. With work as central to an area as
Peter's, it is also almost impossible, in a reasonable amount of space,
to mention all other authors whose work is relevant. Because of that,
I deliberately decided against trying to write a historical article: ref-
erences to other authors are kept to the minimum needed. Let this be
an apology to those who are not quoted.
Peter's work helped define the subject of stable homotopy theory.
His contributions are both foundational and calculational, and concern
virtually all branches of the field. Perhaps his most significant contri-
bution is in the search for concepts. It is my view that very much like
natural science, mathematics investigates real phenomena of nature.
Unlike the objects of natural science, however, these phenomena are
not directly perceptible, but our understanding of them takes the form
of concepts. Definitions are used to attain these concepts.
A major portion of Peter's work is precisely in developing the con-
cepts for stable homotopy theory and unifying them if different versions
of the concepts exist. Examples are the very notion of a spectrum, in-
finite loop space theory, and later algebraic structures on spectra. The
result of such effort is that in algebraic topology, we have a clear pic-
ture of the concepts we are studying. This is necessary in order for
an area to be successful: while mathematical intuition may bypass the
necessity of a clear picture temporarily, the area ultimately needs a
higher degree of resolution to advance.
For the purposes of this paper, I divided Peter's work into 6 areas,
partially by subject, partially chronologically. I list the areas below,
enumerating their major topics. Peter May's complete bibliography
xix
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